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Question

Answers

(a) 8 months

(b) 4 months

(c) 3 months

(d) 6 months

Answer
Verified

Let us start the solution to the above question by letting the time invested by B be x. In business the profit is divided on the basis of contribution to the business, and the contribution is either in form of money or time. In business the contribution is the product of time invested and money invested.

So, the contribution of A is the product of his invested money and invested time which are Rs. 85000 and 12 months, i.e., 1 year respectively.

$ \therefore \text{contribution of A}=12\times 85000 $

Now, the contribution of B is the product of his invested money and invested time which are Rs. 51000 and x months, respectively.

$ \therefore \text{contribution of B}=x\times 51000 $

Now, it is given that the profit was distributed in the ratio of 5:1, i.e., the contribution of A is to B is equal to 5:1.

\[\therefore \dfrac{\text{contribution of A}}{\text{contribution of B}}=\dfrac{5}{1}\]

\[\Rightarrow \dfrac{85000\times 12}{51000\times x}=\dfrac{5}{1}\]

\[\Rightarrow \dfrac{20}{x}=\dfrac{5}{1}\]

Now, if we cross-multiply, we get

\[20=5x\]

\[\Rightarrow x=4months\]