QQuestion
Divide ₹ 21,866 into two parts such that the amount of the first part for 3 years and amount of the second part for 5 years are equal at the same rate of 5% compound interest.
✓Answer
Let the first part be ₹ x and the second part be ₹ (21866 – x) . We have
Amount after 3 years = x(1 + 5\over 100)³ = x(105\over 100)³
Amount after 5 years = (21866 – x)(1 + 5\over 100)5
= (21866 – x)(105\over 100)5
Since these amounts are equal,
x(105\over 100)³ = (21866 – x)(105\over 100)5
x = (21866 – x)(105\over 100)²
⇒ x = (21866 – x)(11025\over 10000)
⇒ 10000x = 21866 × 11025 – 11025 x
⇒ 10000x + 11025 x = 21866 × 11025
⇒ 10000x + 11025 x = 21866 × 11025
⇒ 21025 x = 21866 × 11025
⇒ x = 21866 × 11025 \over 21025
⇒ x = 21866 × 11025 \over 21025 = ₹ 11466
Thus, the first part is ₹ 11,466 and the second part is ₹ 10,400.
Related Questions
More WBBSE Moderate level questions
Aman has taken a loan of ₹ 25,000 for 3 years, in such a way that the compound interest for 1st year, 2nd year and 3rd year is 4%, 5% and 6% p.a. respectively. Find the amount be deposited after 3 years.
The number of smokers is decreasing at the rate of 6 % per year due to publicity of anti-smoking. If at present the number of smokers in a town is 22500, find the number of smokers of that town 2 years ago.
The present population is 13,310. If the population be 17,280 after 3 years, what will be the rate of increase?
Calculate the difference between compound interest and simple interest on Rs. 20,000 for 2 years at 5% per annum.
In how many years will Rs. 500 get Rs. 105 compound interest at 10% per annum compound interest?
The sum of Principal and Compound interest in certain time is called ___.
If the rate of simple interest and compound interest are both 10% per annum, then the ratio of simple interest and compound interest in second year of a certain principal will be - (a) 20 : 21 (b) 10 : 11 (c) 5 : 6 (d) 1 : 1
State True or False: In the compound interest if the rate of interest in the first three years is r1,%, r2%, 2r3% respectively, then the amount for the principal P at the end of three years is P
What will be the compound interest and simple interest for one year at the fixed rate of interest on a fixed sum of money?
State True or False: The relation between principal and amount is Principal < Amount.
The annual rate of compound interest is r% and if the first year principal is P, then the 2nd year principal is ___.
At present the population of a village is P and if rate of increase of population per year be r %, after n years the population will be: (a) P (1 + )n (b) P (1 + )n (c) P (1 + )2n (d) P (1 - )n