Question

A began a business with Rs. 85,000. He was joined afterwards by B. With Rs. 51,000. For how much period does B join, if the profits at the end of the year are divided in the ratio of 5:1?
(a) 8 months
(b) 4 months
(c) 3 months
(d) 6 months

Answer 1

Hint: Let us start the solution by letting the time invested by B be x. In practical life we consider time is equivalent to money and it is given that they got the same share of the profit, that means in some or the other way they have contributed equally. The contribution to a business is equal to time multiplied by money, so take the ratio of the product of the investment and time of both A and B to get the answer and equate it with 5:1 to get the answer.

Complete step-by-step answer:
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
\[20=5x\]
\[\Rightarrow x=4months\]
So, the correct answer is “Option B”.

Note: If you find it difficult to understand, you can think of it as a person who invests more time have to invest less money and a person who invests less time must invest more money, so we can say that time and money invested are inversely proportional to each other. Now use the constant of proportionality to remove the proportionality sign and use the conditions given in the question to reach the answer.