Moderate 686 likes

Question

If 15 farmers can cultivate 18 bighas of land in 5 days, determine by using the theory of variation the number of days required by 10 farmers to cultivate 12 bighas of land.

WBBSE Class X Mathematics Variation 03 Mark 2022

Answer

No. of farmers = A, no. of days = B & area of land = C

No. of days is in inverse variation with no. of farmers, when area of land remains constant

i.e., B ∝ \frac{1}{A} when C is constant

Again, No. of days is indirect variation with area of land; when No. of farmers remains constant

∴ B ∝ C when A is Constant.

According to the theorem on joint variation,

B ∝ \frac{C}{A} when C & A both vary

∴ B = K \frac{C}{A} where K is a constant of variation.

Given A = 15, B = 5, & C = 18.

5 = K \frac{18}{15}

or, K =   \frac{15 \times 5}{18} = \frac{25}{6}

⇒ B = K \frac{C}{A}

⇒ B = \frac{25}{6} \times \frac{12}{10} = 5

∴ No. of days = 5.

Related Questions

More WBBSE Moderate level questions

1/12
Moderate
Q. How can the given conversion be carried out?
A. The given conversion of ethene (H₂C = CH₂) to ethane (H₃C –...
Moderate
Q. State the resistance of 220 V – 100 W bulb
A. Power (P) = Resistance (R) = = = = 484 Ω
Moderate
Q. For which value of the angle of incidence in refraction of light is Snell’s law...
A. Snell’s law is not applicable when the angle of incidence is 0°.
Moderate
Q. Write whether the following statement is true or false: If coefficient of linear expansion of...
A. True Explanation: Coefficient of cubical expansion γ = 3 × coefficient of...
Moderate
Q. What is the number of molecules present in 16 g of O₂ at S.T.P.?
A. 3.011 × 10²³ Explanation: Given mass = 16 g Molecular mass =...
Moderate
Q. Write whether the following statement is true or false: According to Charles’ law, at (–)...
A. False Explanation: Charles' law states volume becomes zero at absolute zero (-273°C),...
Moderate
Q. Write the name of monomer of a polymer which is used to prepare non-stick utensils.
A. Tetra fluoro ethylene Explanation: Polytetrafluoroethylene (PTFE or Teflon) is used for non-stick...
Moderate
Q. Write down the IUPAC name of the following organic compound
A. 2-Bromopropane or (1) CH₃–CH₂–CH₂–OH → Propane-1-ol(2) CH₃–CH(OH)–CH₃ → Propane-2-ol
Moderate
Q. Name the metal which is extracted in thermite process.
A. Fe Explanation: Thermite process reduces metal oxides using Al at high temperature...
Moderate
Q. Fill up the blank: CaC₂ + N₂ → ____ + C
A. CaNCN / CaCN₂ (Calcium cyanamide) Explanation: Haber's process uses Fe as catalyst...
Moderate
Q. What happens when an iron spoon is dipped into acidified copper sulphate solution?
A. When an iron spoon is dipped into acidified copper sulphate solution, a...
Moderate
Q. Left Column 2.2.1 Metal present in German silver 2.2.2 A transuranium element 2.2.3 The metal...
A. 2.2.1 – (d), 2.2.2 – (c), 2.2.3 – (b), 2.2.4 – (a).​...