Chapter – 10 : Profit And Loss | Chapter Solution Class 9

Ganit Prakash Solution 9

Book Name	: Ganit Prakash
Subject	: Mathematics (Maths)
Class	: 9 (Madhyamik/WB)
Publisher	: Prof. Nabanita Chatterjee
Chapter Name	: Profit And Loss (10th Chapter)

Let us work out – 10.1

1. Let us fill up the following table:

	Cost Price	Selling Price	Profit / Loss	Percentage Profit / Loss
(i)	Rs. 500			Profit is 25
(ii)	Rs. 300			Loss is 7
(iii)	Rs. 1250			Loss is 8
(iv)		Rs. 23000		Profit is 15

Solution:

(i) $\text { Selling price } =\frac{100+\mathrm{P} \%}{100} \times \text { Cost Price }$

$=\frac{100+25}{100} \times 500 \\$

$=\frac{125}{1\cancel{00}} \times 5\cancel{00} \\$

$=\text { Rs. } 625 \text { (Ans.) } \\$

$\therefore \text { Profit } =\text { Selling price - Cost Price } \\$

$=625-500=\text { Rs. } 125 \text { (Ans.) }\\$

(ii) $\text { Selling price } =\frac{100-\mathrm{L} \%}{100} \times \mathrm{C}. \mathrm{P} \\$

$=\frac{100-7}{100} \times 300 \\$

$=\frac{93}{1\cancel{00}} \times 3\cancel{00} \\$

$=\text { Rs. } 279 \\$

$\therefore \text { Loss }=\text { C.P }- \text { S.P } \\$

$=300-279 \\ =\text { Rs. } 21 \text { (Ans.) }\\$

(iii) $\text { Selling price }=\frac{100-\mathrm{L} \%}{100} \times \mathrm{C} \mathrm{P} \\$

$=\frac{100-8}{100} \times 1250 \\$

$=\frac{{ }^{46} \cancel{92}}{\cancel{100}_{\cancel2}} \times{ }^{25} \cancel{1250} \\$

$\text { = Rs. } 1150 \text { (Ans.) } \\$

$\text { Loss }=\text { C.P - S.P } \\$

$=1250-1150=\text { Rs. } 100 \text { (Ans.) } \\$

(iv) $\text { Cost price } =\frac{100}{100+P \%} \times \text { S.P } \\$

$=\frac{100}{100+15} \times 23000 \\$

$=\frac{100}{\cancel{115}} \times \cancel{23000}^{200} \\$

$=\text { Rs. } 20000 \text { (Ans.) } \\$

$\text { Profit } =\text { S.P - C.P } \\$

$=23000-20000=\text { Rs. } 3000 \text { (Ans.) }\\$

2. From the graph, let us find out the answers of the following question:

(a) Let us write the relation between cost price and selling price by observing the graph.

(b) Let us write the selling price if the production cost of the jute bag is Rs. 60

(c) Let us write the production cost if the selling price of the jute bag is Rs. 125. by observing the graph.

(d) Let us calculate and write the percentage profit/loss from the graph.

(e) Let us write the percentage of profit/loss on selling price from the graph.

Solution: Given:

(a) From the graph, Cost price and selling price are in proportion.

(b) From the graph, We see that, Selling price of the Jute bag $= Rs. 75$

Cost price of the Jute bag $= Rs. 100\\$

(d) We take,

$\text { C.P } =40, \quad \text { S.P. }=50 \\$

$\text { Profit\% } =\text { S.P }- \text { C.P } \\$

$=50-40=10 \\$

$\text { Profit } =\frac{P}{\text { C.P }} \times 100 \\$

$=\frac{1\cancel0}{4\cancel{00} } \times 1\cancel{00}^{25} \\$

$=25 \% \text { (Ans.) }\\$

(e) $\text { Profit\% on S.P } \\$

$=\frac{\mathrm{P}}{\mathrm{SP}} \times 100 \% \\$

$=\frac{1\cancel0}{\cancel{50}} \times 1\cancel{00} \\$

$=20 \% \text { (Ans.) }\\$

3. Subir uncle has sold a clock at the price Rs. 176. If loss of Subir’s uncle is 12% by selling the clock. Let us calculate and observe that with how much money he has bought the clock.

Solution:

Given:

$\text { S.P } =\text { Rs. } 176 \\$

$L\%=12\%\\$

$\mathrm{C.P} = ?\\$

$\mathrm{C} . \mathrm{P}=\frac{100}{100-\mathrm{L} \%} \times \mathrm{S} . \mathrm{P} \\$

$=\frac{100}{100-12} \times 176 \\$

$=\frac{100}{88} \times 176=200 \\$

$\therefore \quad \text { Cost Price of the clock }=\text { Rs. } 200 \text { (Ans.) } \\$

4. Anoarabibi has old each dozen lemons at Rs. 42 by bying 10 lemons at Rs. 30 . Let us calculate and observe the percentage profit or loss of Anoarabibi has made.

Solution: Given:

S.P of 12 lemons = Rs. 42

$" \ " 1 \ lemon =\frac{\cancel{42}^{7}}{{\cancel{12}^2}}=\frac{7}{2} \\$

C.P of 10 lemons = Rs. 30

$" \ " 1 \ lemon =\frac{\cancel{30}}{\cancel{10}}=3 \\$

Profit = S.P – C.P

$=\frac{7}{2}-3 \\$

$=\frac{7-6}{2}=\frac{1}{2} \\$

$\text { Profit } \% =\frac{P}{C . P} \times 100 \% \\$

$=\frac{2}{3} \times 100 \% \\$

$=\frac{1}{\cancel{2} \times 3} \times 1\cancel{00} \% \\$

$=\frac{50}{3} \%=16 \frac{2}{3} \% \text { (Ans.) }\\$

5. Amalbabu sold a picture at 20% loss. But he made a profit 5% if he sold it with Rs. 200 more. Let us calculate and observe the cost price of the picture he has bought.

Solution:

Let the C.P of the picture be x.

$\therefore$ When loss % = 20%

$\text { S.P } =\frac{100-L \%}{100} \times \text { C.P } \\$

$=\frac{100-20}{100} \times x \\$

$=\frac{80x}{100}\\$

Again,

$\text { Profit } \% = 5 \%\\$

$\text { S.P } =\frac{100+\text { P } \%}{100} \times \text { C.P } \\$

$=\frac{100+5}{100} \times x \\$

$=\frac{105 x}{100}\\$

According to the condition of the problem

$\text { or, } \frac{105 x}{100}-\frac{80 x}{100}=200 \\$

$\text { or, } \frac{105 x-80 x}{100}=200 \\$

$\text { or, } \frac{25 x}{100}=200 \\$

$\text { or, } \frac{x}{4}=200 \\$

$\therefore \quad \mathrm{x}=800, \quad \therefore \quad \text { C.P of the picture }=\text { Rs } 800 \text { (Ans.) } \\$

6. Supriya has bought a clock. If she sells the clock at Rs. 370, her profit will be equal to the loss for selling it at Rs. 210. Let us calculate and write the cost price of the clock.

Solution: Let the C.P of the clock be x

If she sells the clock at Rs. 370,

$\therefore \text { Profit }=370-\mathrm{x}\\$

and if she sells the clock at Rs. 210

$\text { Loss }=x-210\\$

According to the condition of the problem

370-x=x-210 \\[/katex]

$\text { or, }-x-x=-210-370 \\$

$\text { or, }+2 x=+580 \\$

$\text { or } x=\frac{580}{2} \\$

$\therefore \quad x=290 \\$

$\therefore \quad \text { C.P of the clock }=\text { Rs. } 290\\$

7. My elder sister has bought an umbrella from Arun uncle’s shop at Rs. 255. If Arun uncle gave 15% discount on the marcket price, then let us write after calculation the market price of the umbrella.

Solution: $\quad S.P = Rs. 255\\$

$\text { Discount\% } =15 \% \\$

$\text { Market Price } =\frac{100}{100-\text { Discount } \%} \times \text { S.P } \\$

$=\frac{100}{100-15} \times 255 \\$

$=\frac{100}{85} \times 255 \\$

$=300 \\$

$\therefore \quad Market price of the umbrella = Rs. 300 (Ans.)\\$

8. My friend has bought a story book at 25% discount on written price. If he sells the book at written price then let us write the profit percentage after calculation.

Solution: Let the written price be 100

$\therefore \text { Discount }=25 \% \\$

$\therefore \quad \text { S.P }=100=25=75\\$

If he sells the book at written price

Then, profit = 100 – 75 = 25

$\text { Profit } \%=\frac{\mathrm{P} \%}{\text { C.P }} \times 100 \% \\$

$=\frac{25}{75} \times 100 \% \\$

$=\frac{100}{3} \%=33 \frac{1}{3} \% \\(Ans.)\\$

9. Niyamotchacha has bought 150 eggs at the rate of Rs.5 each. But after bringing to the shop, he saw that 8 eggs are broken and 7 eggs are rotten. If he sells each eggs at Rs. 6 then what will be the profit / loss percentage of Niyamotchacha. Let us calculate and write.

Solution: Niyamotchacha has bought 150 eggs at the rate of Rs. 5 each

$\text { C.P of } 150 \text { eggs } =150 \times 5 \\$

$=\text { Rs. } 750 \\$

He saw that 8 eggs are broken and 7 eggs are rotten.

$\text { No. of remaining eggs } =150-(8+7) \\$

$=150-15 \\$

$=135 \text { eggs. }\\$

If he sells each eggs at Rs. 6

$\text { S.P of } 135 \text { eggs }=\text { Rs. } 135 \times 6=\text { Rs. } 810 \\$

$\therefore \quad \text { Profit }=\text { S.P }- \text { C.P } \\$

$=\text { Rs. }(810-750)=\text { Rs. } 60 \\$

$\text { Priofit } \%=\frac{P}{\text { C.P }} \times 100 \% \\$

$\quad \text { Priofit } \%=\frac{60}{750} \times 100 \% \\$

$\therefore \quad \text { Profit } \%=8 \% \text { (Ans.) }\\$

10. Asif chacha sold a toy at 5% profit. If the cost price of the toy is less by 20% and selling price is less by Rs. 34, then Asif chacha would make a 10% profit. Let us calculate the cost price of the toy.

Solution:

Let the Cost price of the toy be x

Profit $\%=5 \% \text { S.P } \\$

$=\frac{100+5}{100} \times x \\$

$=\frac{105 x}{100}=\frac{21}{20} x\\$

If the Cost Price of the toy is less by 20%

$\text { C.P } =\frac{100-20}{100} \times x \\$

$=\frac{80}{100} \times x=\frac{4 x}{5} \\$

$\therefore$ If Asif chacha would make a 10% profit

$\therefore S . P =\frac{100+10}{100} \times \frac{4 x}{5} \\$

$=\frac{110}{100} \times \frac{4 x}{5}=\frac{22 x}{25}\\$

According to the condition of the problem $\quad \frac{21 x}{20}-\frac{22 x}{25}=34 \\$

$\text { or, } \quad \frac{105 x-88 x}{100}=34^{\circ} \\$

$\text { or, } \quad \frac{17 x}{100}=34 \\$

$\text { or, } 17 x=3400, \therefore x=200 \\$

$\therefore \text { Cost Price of the toy }=\text { Rs. } 200 \text { (Ans.) }\\$

11. There is a loss of 4% by selling 12 commodities at Re 1. To make 44% profit how many commodities have to be sold at operator name Re.1?

Solution: By selling 12 commodities at Re.1

Loss%=4%

$" \ " \ " 1 \ commodity \ at \ Re. \frac{1}{12}\\$

$\text { C.P } =\frac{100}{100-4} \times \frac{1}{12} \\$

$=\frac{100}{96} \times \frac{1}{12}=\frac{25}{288}\\$

When profit $\% \ is \ =44 \% \\$

$\text { S.P } =\frac{100+44}{100} \times \frac{25}{288} \\$

$=\frac{144}{100} \times \frac{25}{288}\\$

$=\frac{1}{8} \\$

$\therefore \ In \ Re \ 1 / 8$ , No. of Commodities he sells = 1

” Re. 1 ” ” ” ” ” ” = 1

= 8 (Ans.)

12. By producing two saris, Rama aunt sold one sari at 15% profit and another at 20% profit. She has made total profit by Rs. 262.50. If the ratios of production costs of two saris is 1 : 3, what will be the production cost of each of the two saris?

Solution:

First Sari

Let $C \cdot \dot{P}=x\\$

$\mathrm{P} \%=15 \%\\$

$\text { S.P } =\frac{100+15}{100} \times x \\$

$=\frac{115 x}{100}\\$

$P =\text { S.P - C.P } \\$

$=\frac{115 x}{100}-x\\$

$=\frac{115 x-100 x}{100}\\$

$=\frac{15 x}{100}\\$

Second Sari

Let $C.P =3 \mathrm{x} \\$

$\mathrm{P} \%=20 \%\\$

$\text { S.P } =\frac{100+20}{100} \times 3 \mathrm{x} \\$

$=\frac{120}{100} \times 3 \mathrm{x} \\$

$=\frac{360 \mathrm{x}}{100}\\$

$P =\text { S.P - C.P } \\$

$=\frac{360 x}{100}-3 x \\$

$=\frac{360 x-300 x}{100} \\$

$=\frac{60 x}{100}\\$

According to the condition of the problem,

$\frac{15 x}{100}+\frac{60 x}{100}=262.50 \\$

$\text { or, } \quad \frac{15 x+60 x}{100}=\frac{26250}{100} \\$

$\text { or, } \quad \frac{75 x}{100}=\frac{26250}{100} \\$

$\text { or, } 75 x=26250 \\$

$\text { or, } x=\frac{26250}{75} \\$

$\therefore \quad x=350 \\$

$\therefore \quad \text { C.P of each Sari }=\text { Rs. } 350 \text { (Ans.) }\\$

13. One man bought some toffees at the rate of Rs.2 for 15 pieces. He sold them at the rate of half of money for 5 pieces and the rate of remaining half of money for 10 pieces, What will be his profit / loss percentage?

Solution: Let the total number of toffees be x

$15 \text { Pieces of toffees cost price }=\text { Rs. } 2 \\$

$1 \text { " " " " }=\mathrm{Rs}^{2} / 15 \\$

$\text { x " " " ". =Rs } \frac{2 x}{15} \\$

$5 \text { pieces of toffees selling price } =\operatorname{Re} 1 \\$

$1 \text { " " " " } = \text { Re. } 1 / 5 \\$

$x \text { " " " " } =\text { Rs. } 1 / 5 \times x / 2 \\$

$2 \text { " " " " } =\text { Rs. } x / 10\\$

$10 \text { pieces of toffees selling price }=\text { Re. } 1 \\$

$1 \text { " " " " } = \text { Re. } 1 / 10 \\$

$x \text { " " " " } =\text { Rs. } 1 / 10 \times x / 2 \\$

$2 \text { " " " " } =\text { Rs. } x / 20\\$

$\text { Total S.P } =\frac{x}{10}+\frac{x}{20} \\$

$=\frac{2 x+x}{20}=\frac{3 x}{20}\\$

$\text { Profit }= \text { S.P - C.P } \\$

$=\frac{3 x}{20}-\frac{2 x}{15} \\$

$=\frac{9 x-8 x}{60}\\$

$=\frac{x}{60}\\$

$\text { Profit } \% =\frac{P}{C . P} \times 100 \% \\$

$=\frac{\frac{6}{60}}{2 x} \times 100=\frac{x}{60} \times \frac{15}{2 x} \times 100=\frac{25}{2} \% \\$

$=12 \frac{1}{2} \%(Âns.)\\$

14. Afsar Chacha made two wooden chair with same price and he put the market price for each chair as Rs. 1250. He made a profit of 15% by selling one chair at 8% discount. If he sold the second chair at Rs. 1120, then let us calculate his overall percentage of profit.

Solution: Discount% = 8 %

$\text { S.P. of first chair } =\frac{100-8}{100} \times 1250 \\$

$=\frac{92}{100} \times 1150\\$

$= Rs. 1150 \\$

$\therefore Profit \%=15 \% \\$

$\text { C.P } =\frac{100}{100+15} \times 1150 \\$

$=\frac{100}{115} \times 1250=1000.\\$

$\therefore \quad \text { C.P of two wooden chairs }=\text { Rs. } 2 \times 1000 \\$

$=\text { Rs. } 2000 \\$

$\text { S.P of two wooden chairs = Rs }(1150+1120) \\$

$=\text { Rs. } 2270 \\$

$\text { Profit = S.P - C.P } \\$

$=2270-2000 \\$

$=\text { Rs. } 270 \\$

$\text { Profit } \% =\frac{270}{2000} \times 100 \% \\$

$=\frac{27}{2000} \times 100 \% \\$

$=\frac{27}{2}=13 \frac{1}{2} \% \text { (Ans.) }\\$

15. The Market price of a special type of pen is Rs. 36.50. By selling the pen to Shuvam with a discount of Rs.2.90 Rafique Chacha makes a profit of 12%. If he sold a pen of that type to Mita at Rs. 34.50, then let us find out his percentage profit in the second pen.

Solution:

Market price of pens = Rs. 36.50

Discount = Rs. 2.90

$\therefore \quad \text { S.P of Shuvam } =\text { Rs. }(36.50-2.90) \\$

$=\text { Rs. } 33.60\\$

$\text { C.P of Rafique Chacha } =\frac{100}{100+12} \times 33.60 \\$

$=\frac{100}{112} \times 33.60\\$

$\text { = Rs. } 30\\$

If he sold pen of that type to Mita at Rs. 34.50

$\therefore \quad \text { Profit } \% =\text { Rs. }(34.50-30) \\$

$=\text { Rs. } 4.50 \\$

$\text { Profit } \% =\frac{4.50}{30} \times 100 \% \\$

$\text { Profit } \% =\frac{450}{30 \times 100} \times 100 \% \\$

$=15 \% \text { (Ans.) }\\$

16. A publisher expended Rs. 3,875 for buying papers, Rs. 3,315 for printing and Rs. 810 for binding of 2000 copies books. He sold to book sellers and makes a profit 20% after giving a discount of 20%. Let us determine the market price of each book.

Solution: Total C.P of 2000 copies books

$=\text { Rs. }(3,875+3315+810) \\$

$=\text { Rs. } 8,000\\$

$\therefore \text { C.P of } 1 \text { book }=\text { Rs. } \frac{8000}{2000}=\text { Rs. } 4$

$\text { Profit } \%=20 \%\\$

$\therefore \text { S.P } =\text { Rs. } \frac{100+20}{100} \times 4 \\$

$= \text { Rs. } \frac{120}{100} \times 4 \\$

$=\text { Rs. } \frac{48}{10}\\$

$\therefore \text { Discount } \%=20 \% \\$

$\therefore \quad \text { Market Price }=\text { Rs. } \frac{100}{100-20}=\text { Rs. } 4.80 \\$

$=\text { Rs. } \frac{100}{80} \times \frac{480}{100} \\$

$=\text { Rs. } 6 \\$

$\therefore \quad$ Market price of each book = Rs. 6 (Ans.)

17. Hasimabibi sold each of two handloom factories at Rs. 1248. She makes a profit of 4% for the first, but makes a loss for 2nd. What is her overall profit or loss?

Solution: First handloom factory

$\text { S.P = Rs. } 1248\\$

$Profit \%=4 \% \\$

$\text { C.P } =\text { Rs. } \frac{100}{\frac{100+4}{4}} \times 1248 \\$

$=\text { Rs. } \frac{100}{104} \times 1248 \\$

$=\text { Rs. } 1200\\$

Second handloom factory

$\text { S.P = Rs. } 1248 \\$

$\text { Loss } \%=4 \% \\$

$\text { C.P }=\text { Rs. } \\$

$\frac{100}{100-4} \times 1248 \\$

$=\operatorname{Rs} . \frac{100}{96} \times 1248 \\$

$\text { = Rs. } 1300 \\$

$\text { Total C.P of two factories }=\text { Rs. }(1200+1300) \\$

$=\text { Rs. } 2500 \\$

$\text { Total S.P of two factories = Rs. } 2 \times 1248 \\$

$=\text { Rs. } 2496 \\$

$\text { Loss = C.P - S.P = Rs. }(2500-2496) \quad=\text { Rs. } 4 \text { (Ans). } \\$

18. Karim makes a loss of 19% by selling a mobile phone to Mohan at Rs.4860. If Mohan sells to Rahim at the same price in which Karim sells to Mohan, then Karim makes a profit of 17%. What is the percentage profit of Mohan?

Solution: Karim makes a loss of 19% $\text { S.P of Karim }=\text { Rs. } 4860 \\$

$\text { C.P of Karim }=\text { Rs. } \frac{100}{100-19} \times 4860 \\$

$=\text { Rs. } \frac{100}{81} \times 4860\\$

If Karim makes a profit of 17%

$\text { S.P } =\text { Rs. } \frac{100+17}{100} \times 6000 \\$

$=\text { Rs. } \frac{117}{100} \times 6000 \\$

$=\text { Rs. } 7020\\$

$\therefore \text { Profit of Mohan }=\text { Rs. }(7020-4860) \\$

$\text { = Rs. } 2160 \\$

$\text { Profit } \%=\text { Rs. } \frac{2160}{4860} \times 100 \% \\$

$=\text { Rs. } \frac{400}{9} \%=44 \frac{4}{9} \% \\$

19. Firoz Chacha got total Rs. 719.50 by selling a pant at 20% profit and shirt at 15% profit. If he would sell the pant at 25% profit and shirt at 20% profit, then he would get Rs. 30.50 more. Let us calculate the cost prices of the pant and shirt.

Solution:

Method – I

Total selling price = 719.50

Let the selling price of pant be x

and $\text{" " " " " "} \ shirt \ be \ (719.50-x) \\$

1st. Case

S.P of pant = x

$Profit \%=20 \% \\$

$C. P =\frac{100}{100+20} \times x \\$

$=\frac{100 x}{120}=\frac{5 x}{6}\\$

$S.P of Shirt = 719.50 - x$

$Profit \%=15 \% \text { C.P }\\$

$=\frac{100}{100+15}(719.50-\mathrm{x}) \\$

$=\frac{100(719.50-\mathrm{x})}{115} \\$

$=\frac{14390-20 \mathrm{x}}{23}\\$

2nd. Case

$\text { C.P of pant }=\frac{5 x}{6}\\$

$Profit \%=25 \% \\$

$S.P=\frac{100+25}{100} \times \frac{5 x}{6} \\$

$=\frac{125}{100} \times \frac{5 x}{6} \\$

$=\frac{25 x}{24} \\$

$\text { C.P of Shirt }=\frac{14390-20 x}{23}\\$

$Profit \%=20 \%\\$

$\text { S.P }=\frac{100+20}{100} \times \frac{14390-20 x}{23} \\$

$=\frac{120}{100} \times \frac{14390-20 x}{23} \\$

$=\frac{86340-120 x}{115} \\$

According to the condition of the problems,

$\frac{25 x}{24}+\frac{86340-120 x}{115}=719.50+30.50 \\$

$\text { or, } \frac{2875 x+2072160-2880 x}{2760}=750 \\$

$\text { or, } \frac{2072160-5 x}{2760}=750 \\$

$\text { or, } 2072160-5 x=2070000 \\$

$\text { or, }-5 x=2070000-2072160 \\$

$\text { or, }\cancel{-}5 x=\cancel{-}2160 \\$

$\text { or, } x=\frac{2160}{5} \\$

$\therefore \quad x=432 \\$

$\text { C.P of Pant }=\frac{25 x}{6}=\frac{5 \times 432}{6}=360 \\$

$\text { C.P of Shirt }=\frac{14390-20 \mathrm{x}}{23} \\$

$=\frac{14390-20 \times 432}{23} \\$

$=\frac{5750}{23} \\$

= 250

$\therefore \quad \text { C.P of pant }=\text { Rs. } 360 \\$

$\text { C.P of Shirst = Rs. } 250 \text { (Ans) } \\$

Method-II

Let the Cost Price of Pant be x and Cost Price of Shirt be y

$\text { Pant } \\$

$\mathrm{CP}=\mathrm{x} \\$

$\therefore \quad \text { Profit } \%=20 \% \\$

$\text { S.P }=\frac{100+P}{100} \times \text { C.P } \\$

$\text { S.P }=\frac{100+20}{100} \times x \\$

$\text { S.P }=\frac{120 x}{100} \\$

$\text { Shirt } \\$

$\mathrm{CP}=\mathrm{y} \\$

$\therefore \quad \text { Profit } \%=15 \% \\$

$\text { S.P }=\frac{100+P}{100} \times \text { C.P } \\$

$\text { S.P }=\frac{100+15}{100} \times y \\$

$\text { S.P }=\frac{115 y}{100} \\$

According to the condition of the problem

$\frac{120 x}{100}+\frac{115 y}{100}=719.50 \\$

$\text { or, } \frac{120 x+115}{100}=\frac{71950}{100} \\$

$\text { or, } 120 x+115 y=71950 \ldots \ldots \text { (i) }\\$

Again,

$\text { Pant } \\$

$\mathrm{CP}=\mathrm{x} \\$

$\therefore \quad \text { Profit } \%=25 \% \\$

$\text { S.P }=\frac{100+25}{100} \times \mathrm{x} \\$

$\text { S.P }=\frac{125 \mathrm{x}}{100}\\$

Shirt

$\mathrm{CP}=\mathrm{y}\\$

$\therefore \text { Profit } \%=20 \% \\$

$\text { S.P }=\frac{100+20}{100} \times y \\$

$\text { S.P }=\frac{120 y}{100}\\$

According to the condition of the problem

$\frac{125 x}{100}+\frac{120 y}{100}$

$=71950+30.50 \\$

$\text { or, } \frac{125 x+120 y}{100}=\frac{750}{100}\\$

$\text { or, } 125 x+120 y=7500 ............. (ii) \\$

$\therefore \quad 125 x+115 y=71950 ............... (i) \times 25 \\$

$125 x+120 y=75000 ............... (ii) \times 24 \\$

or, $\quad 3000 x+2875 y=1798750\\ \underline{\quad-3000 x+2880 y=1800000}\\ \underline{(by Subtracting) \cancel{-}5 y= \cancel{-}1250} \\$

$y=\frac{\cancel{1250}}{\cancel{5}} \\$

y = 250

Now putting the value of y in equation (i)

$120 x+115 y=71950\\$

or, $120 x+115 \times 25=71950 \\$

or, $120 \mathrm{x}+28750=71950 \\$

or, $120 \mathrm{x}=71950-28750 \\$

or, $120 x=43200 \\$

or, $x=\frac{4\cancel{3200}}{1\cancel{2}0} \\$

$\therefore \quad \mathrm{x}=360 \\$

$\text { Cost price of the Pant }=\text { Rs } 360 \\$

$\text {Cost price of the Shirt } =\text { Rs. 250 } (Ans)\\$

20. Rabi uncle bought rice at Rs. 3000 . He sold 1/3rd part of rice at 20% loss and 2/5 th part of rice at 25% profit At what percentage profit, the remaining part of rice is t sold te get overall 10% profit.

Solution: $\quad C.P of Rice = Rs. 3000\text { Profit } \%=10 \% \\$

$\text { S.P } =\text { Rs. } \frac{100+10}{100} \times 3000 \\$

$=\frac{110}{100} \times 3000 \\$

$=\text { Rs. } 3300\\$

1st. Case

$\text { 1/3rd of rice cost }=\frac{1}{3} \times 3000=\text { Rs. } 1000 \\$

$\text { Loss } \%=20 \% \\$

$\text { S.P }$

$=\text { Rs. } \frac{100-20}{100} \times 1000 \\$

$=\frac{80}{100} \times 1000 \\$

$=\text { Rs. } 800\\$

2nd. Case

$\frac{2}{5} \text { th. of rice cost }=\frac{2}{5} \times 3000=\text { Rs. } 1200\\$

$Profit \%=25 \%\\$

$\text { S.P } =\text { Rs. } \frac{100+25}{100} \times 1200 \\$

$=\frac{125}{100} \times 1200 \\$

$=\text { Rs. } 1500\\$

$\text { Remaining Profit } =\text { Rs. }\{3000-(1000+1200)\} \\$

$=\text { Rs. }(3000-2200) \\$

$=\text { Rs. } 800\\$

$\text { S.P } =\text { Rs. }\{3300-(800+1500)\} \\$

$=\text { Rs. }(3300-2300) \\$

$=\text { Rs. } 1000 \\$

$\therefore \text { Profit } \%=\text { S.P }- \text { C.P } \\$

$=\text { Rs. }(1000-800)=\text { Rs. } 200 \\$

$\text { Profit } \%=\text { Rs. } \frac{2004}{800} \times 100 \\$

$=25 \% \text { (Ans.) }\\$

21. A trader by selling one kind of tea at Rs. 80/Kg . makes a loss of 20% and makes a profit of 25% by selling another kind of tea at Rs. 200/Kg . At what ratio these two types of tea should be mixed so that by selling it at Rs. 150/Kg. the profit would be 25% ?

Solution: Let x kg one kind of tea sell at Rs. 80/Kg makes a

loss of 20% and y/Kg . of another kind of tea sells at Rs 200/Kg, makes a profit of 25% .

1st. Tea.

$\text { S.P }=80 \times x=80 \mathrm{x}\\$

$Loss \%=20 \%\\$

$\text { C.P } =\frac{100}{100-20} \times 80 \mathrm{x} \\$

$=\frac{100}{80} \times 80 \mathrm{x} \\$

$=100 \mathrm{x}\\$

2nd. Tea.

$\text { S.P }=200 \times y=200 y\\$

$Profit \%=25 \%\\$

$C.P =\frac{100}{100+25} \times 200 y \\$

$=\frac{100}{125} \times 200 y \\$

= 160y

Mixed Tea.

$\text { S.P }=150(\mathrm{x}+\mathrm{y})\\$

$Profit \%=25 \% \\$

$\text { Total C.P }=(100 \mathrm{x}+160 \mathrm{y}) \\$

$\text { S.P }=\frac{100+25}{100}(100 x+160 y) \\$

$=\frac{125}{100}(100 x+160 y) \\$

$=\frac{5}{4} \times 20(5 x+8 y) \\$

$=25(5 x+8 y) \\$

According to the condition of the problem,

$or, 25(5 x+8 y)=150(x+y) \\$

$or, 5 x+8 x=6 x+6 y\\$

$\text { or, } 6 x-5 x=8 y-6 y \\$

$\text { or, } x=2 y \\$

$\text { or, } \frac{x}{y}=\frac{2}{1} \\$

$\therefore \quad x: y=2: 1 \\$

$\therefore \quad \text { Required ratio }=2: 1 \text { (Ans.) }\\$

Let us work out – 10.2

1. Sabalbabu of Antpur, by producing rice sells it to a whole saler Sahanabibi at 20% profit. Sahanabibi sells that rice to the shopkeeper Utpal babu at 10% profit. But if Utpal babu sells this rice at

12% profit, then let us find out the answers of the following questions by drawing picture on a straight line.

(i) Subal babu spent Rs. 7500 to produce some amount of rice. Let us calculate and write it with how much money Sahanabibi has bought that amount of rice.

(ii) To produce the some amount of rice Sabal babu has spent Rs. 2500, with how much money Utpal babu has spent Rs. 2500, with how much money Utpalbabu will sell that amount of rice. Let us calculate and write it.

(iii) The price at which Utpal babu sells rice to us, if Sabalbabu sells directly at that rice then what will be the profit percentage of Subalbabu. Let us calculate and write it.

Solution: (i) C.P of Subal babu = Rs. 7500

$Profit \%=20 \% \\$

S.P of Subal babu = C.P of Sahanabibi

$=\frac{100+20}{100} \times 7500 \\$

$=\frac{120}{100} \times 7500 \\$

$=\text { Rs. } 9000 \text { (Ans.) }\\$

(ii) C.P of Subal babu = Rs. 2500

$Profit \%=20 \%\\$

S.P of Subal babu = C.P of Sahanabibi $=\frac{100+20}{100} \times 2500 \\$

$=\frac{120}{100} \times 2500 \\$

$=\text { Rs. } 3000\\$

$Profit \%=10 \% \\$

S.P of Sahanibibi = C.P of Utpal babu

$=\frac{100+10}{100} \times 3000 \\$

$\therefore Profit \%=10 \% \\$

$=\frac{110}{100} \times 3000 \\$

$=\text { Rs. } 3300\\$

$\text { S.P of Utpal balu } =\frac{100+12}{100} \times 3300 \\$

$=\frac{112}{100} \times 3300 \\$

$=\text { Rs. } 3696\\$

(iii) $\text { Profit } =\text { Rs. }(3696-2500) \\$

$=\text { Rs. } 1196 \\$

$\text { Profit } \% =\frac{1196}{2500} \times 100 \\$

$=\frac{1196}{25} \%=47 \frac{21}{25} \% \text { (Ans.). }\\$

2. In a bazar, at the time of selling jute bag, the producer, whole saler and retailer make profits of 15%, 20% and 25% respectively. Now if a bag reaches to buyer through producer, wholesaler and retailer, then let us find out the answers of the following questions –

(i) Let us calculate and write the production cost of a bag which is bought by c buyer at Rs. 138.

(ii) Let us calculate and write the price of the bag at which the buyer will buy when its production cost is Rs. 140.

(iii) The bag which a retailer has bought at Rs. 98, let us calculate and write that how much money will be given by buyer for that bag.

(iv) The bag which the wholesaler has bought at Rs.175, let us calculate and write that how much money, a buyer will give to buy that bag.

(v) The bag which a buyer has bought at Rs. 276 if that bag would have been bought directly from the wholesaler then how money would be saved. Let us calculate and write it.

Solution: (i) C.P of buyer = S.P of retailer = Rs. 138

C.P of retailer = S.P of wholesaler $=\frac{100}{100+25} \times 138 \\$

$=\frac{100}{125} \times 138 \\$

$=\operatorname{Rs} \cdot \frac{552}{5} \\$

$\therefore \quad$ C.P of whole saler = S.P of producer $=\frac{100}{100+20} \times \frac{552}{5} \\$

$=\frac{100}{120} \times \frac{552}{5} \\$

$=\text { Rs.92 }\text { C.P of Producer } =\frac{100}{100+15} \times 92 \\$

$=\frac{100}{115} \times 92 \\$

$\therefore$ The price of the bag = Rs. 80 (Ans.)

(ii) C.P of producer = Rs. 140

S.P of producer = C.P of wholesaler.

$=\frac{100+15}{100} \times 140 \\$

$=\frac{115}{100} \times 140 \\$

$=\text { Rs. } 161 \\$

$\text { C.P of whole saler } =\text { C.P of retailer } \\$

$=\frac{100+20}{100} \times 161 \\$

$=\frac{120}{100} \times 161 \\$

$=\text { Rs. } \frac{1932}{10}\\$

$\text { S.P of retailer } = \text { C.P of buyer }\\$

$=\frac{100+25}{100} \times \frac{1932}{10} \\$

$=\frac{125}{100} \times \frac{1932}{10} \\$

$=\operatorname{Rs} . \frac{438}{2} \\$

$=\text { Rs. } 241.50 \text { (Ans.) }\\$

(iii) $\text { C.P of retialer } = Rs. 98\\$

$\text { S.P of retailer } =\frac{100+25}{100} \times 98 \\$

$=\frac{125}{100} \times 98 \\$

$=\frac{245}{2}=\text { Rs. } 122.50 \\$

$\therefore \quad \text { S.P of retailer } = \text { C.P of buyer } = Rs. 122.50 (Ans.)\\$

(iii) $\text { C.P of retialer } = Rs. 175\\$

$\text { S.P of Wholesaler } = \text {C.P of retailer}\\$

$\text { S.P of retailer }=\frac{100+20}{100} \times 175 \\$

$=\frac{120}{100} \times 175 \\$

$=\frac{\text { Rs. } 210}{10} \\$

$\therefore \quad \text { C.P of retailer }=\text { Rs. } 210\\$

(v) $\text { C.P of buyer }\\$

$=\text { Rs. } 276 \\$

$\text { S.P of retailer } =\text { R. } 276 \\$

$\text { C.P. of retailer } =\text { S.P of Whotesaler. } \\$

$=\frac{100}{100+25} \times 276 \\$

$=\frac{100}{125} \times 276 \\$

$=\frac{1104}{5} \\$

$=\text { Rs. } 220.80 \\$

$\therefore \quad \text { He saves } =\text { Rs. } 276-\text { Rs. 220.8 } \\$

$=\text { Rs. } 55.20 \text { (Ans.) }\\$

3. The production cost and the cost price of a cycle at different level are –

Production Cost (Rs.)	Cost Price of Wholesaler (Rs.)	Cost Price of Retailer (Rs.)	Cost Price of Buyer (Rs.)
1050	1260	1149	1666.35

(i) Let us calculate, by selling cycle, how much profit percentage, the retailer has made.

(ii) Let us calculate and observe that by selling cycle, what is the profit percentage, the wholesaler has made.

(iii) Let us calculate and write the profit percentage, that the producer has made by selling cycle.

(iv) Let us calculate and write that how much profit percentage has to be given more by a buyer than the production cost to buy a cycle.

(v) If a buyer buys a cycle directly from the producer and the producer has a profit of 30%, then how much money, the buyer will save. Let us calculate and write it.

Solution: (i) Profit of the retailer = Rs. (666.35-1449)

$\text { = Rs, } 217.35 \\$

$\text { Profit } \%=\frac{217.35}{1449} \times 100 \% \\$

$=\frac{21735}{1449 \times 100} \times 100 \\=15 \% \\$

(ii) $\text { Profit of whole saler } =\text { Rs. }(1449-1260) \\$

$=\text { Rs } 189 \\$

$\text { Profit } \% =\frac{189}{1260} \times 100 \% \\$

$=15 \% \text { (Ans) }\\$

(iii) $\text { Profit of producer }=\text { Rs. }(1260-1050) \\$

$=\text { Rs. } 210 \\$

$\text { Profit } \%=\frac{210}{1050} \times 100 \% \\$

$=20 \% \text { (Ans) } \\$

(iv) Profit of producer to be given more by buyer

$= \text { Rs. }(1666.35-1050) \\$

$=\text { R. } 616.35 \\$

$\text { Profit } \%\\$

$=\frac{616.35}{1050} \times 100 \% \\$

$=\frac{61635}{1050 \times 100} \times 100 \\$

$=\frac{587}{10} \\$

$=58.7 \% \text { (Ans.) }\\$

(v) S.P of producer = C.P of buyer

$=\frac{100+30}{100} \times 1050 \\$

$=\frac{130}{100} \times 1050 \\$

= Rs. 1365 He saves = Rs. (1666.35 – 1365)= Rs. 301.35 (Ans.)

4. M.C.Q:

(i) The ratio of cost price and selling price is 10 : 11, the profit percentage is

(a) 9

(b) 11

(c) $10 \frac{1}{9}$

(d) 10

Solution: Let C.P = 10 x

$\text { S.P }=11 \mathrm{x} \\$

$P = S . P-\text { C.P } \quad=11 \mathrm{x}-10 \mathrm{x}=\mathrm{x}\\$

$\text { Profit } \%$

$=\frac{P}{\text { C.P }} \times 100 \% \\$

$=\frac{\mathrm{x}}{10 \mathrm{x}} \times 100 \% \\$

= 10%

$\therefore \quad$ (d) is correct option

(ii) Buying a book at Rs.40 and selling it at Rs. 60, the profit percentage will be

(a) 50

(b) $33 \frac{1}{3}$

(c) 20

(d) 30

Solution: $\text { Profit } =\text { Rs. }(60-40) \\$

$=\text { Rs. } 20\\$

$\text { Profit } \%=\frac{20}{40} \times 100 \% \\$

= 50%

$\therefore \quad$ (a) is correct option

(iii) A shirt is sold at Rs. 360 and there is a loss of 10%. The cost price of the shirt is

(a) Rs. 380

(b) Rs. 400

(c) Rs. 420

(d) Rs.450

Solution: $\text { S.P } =\text { Rs. } 360 \\$

$\text { Loss } =10 \% \\$

$\text { C.P } =\frac{100}{100-10} \times \text { S.P } \\$

$=\frac{100}{90} \times 360 \\$

$=\text { Rs. } 400 \\$

$\therefore$ (b) is correct option

(iv) After 20% discount, the selling price of a geometry box becomes Rs.48. The market price of the geometry box is

(a) Rs. 60

(b) Rs. 75

(c) Rs. 80

(d) Rs. 50

Solution: Market price

$=\frac{100}{100-20} \times 48 \\$

$=\frac{100}{80} \times 48 \\$

$=\operatorname{Rs} 60 \therefore \quad$ (a) is correct option

(v) A retailer buys medicine at 20% discount on market price and sells to buyer at market price. The retailer makes a profit percentage

(a) 20

(b) 25

(c) 10

(d) 30

Solution: Let M.P = 100 $\text { Discount }=20 \% \\$

$\text { C.P }=\text { Rs. }( 100-20)=\text { Rs. } 80, \text { S.P }=\text { Rs. } 100 \\$

$\text { Profit } =\text { Rs }(100-80) \\$

$=\text { Rs. } 20 \\$

$\text { Profit } \%=\frac{20}{80} \times 100 \% \\$

= 25%

$\therefore \quad$ (b) is correct option

5. Short answer type questions:

(i) If 20% profit is on cost price, what is profit percentage on selling price?

Solution: Let C.P =100 , Profit % = 20 %

$\text { S.P }=100+20=120\\$

$\therefore \text { Profit } \% \text { on S.P } =\frac{\mathrm{P}}{\mathrm{S}\\ \mathrm{P}} \times 100 \% \\$

$=\frac{20}{120} \times 100\\$

$=\frac{50}{3} \\$

$=16 \frac{2}{3} \% \text { (Ans.) }\\$

(ii) If 20% profit on selling price what is the profit percentage on cost price?

Solution: Let S.P = 100

Profit % = 20 %

$\therefore \quad \text { C.P }=100-20=80\\$

$\therefore \text { Profit } \% \text { on C.P } =\frac{20}{80} \times 100 \% \\$

$=25 \% \text { (Ans.) }\\$

(iii) By selling 110 mangoes, if the cost price of 120 mangoes has been got, what will be the profit percentage?

Solution:

Let the cost price of 1 mango be Re.1

then, $\text{" " "}$ 110 mangoes Rs. 110

But S.P of 110 mangoes = C.P of 120 mangoes

= Rs. 120

$\therefore \quad Profit = Rs. (120-110)= Rs. 10\\$

$\text { Proft }\%=\frac{10}{110} \times 100 \% \\$

$=\frac{100}{11} \\$

$=9 \frac{1}{11} \% \text { (Ans.) }\\$

(iv) To submit electricity bill in due time, 15% discount can be obtained. Sumonbabu has got Rs. 54 as discount for submission of electricity bill in due time. How much was his electricity bill?

Solution: Let the amount of electricity bill be x

then, $\quad 15 \%, of x=54 \\$

or, $\frac{15}{100} \times x=54 \\$

or, $\frac{x}{20}=18 \\$

$\therefore \quad x=360 \\$

$\therefore$ Amount of electricity bill = Rs. 360 /-

(v) A commodity is sold at Rs. 480 with a loss of 20% on selling price, what is the cost price of the commodity?

Solution: $\text { S:P }=\text { Rs.480 } \\$

$\text { Loss }=20 \% \\$

$\text { C.P }=\frac{100}{100-20} \times 480 \\$

$=\frac{100}{80} \times 480 \\$

$= \text { Rs. } 600 \\$