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A started a business with Rs. 21000 and is joined afterwards by B with Rs. 36000. After how many months did B join if the profit at the end of the year are divided equally?
(a) 3
(b) 4
(c) 5
(d) 6

Last updated date: 15th Jul 2024
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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 equate the product of the investment and time of both A and B 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.
Now in the above question, it is given that both A and B got the same amount of profit, meaning both have contributed equally. The money invested by A is Rs. 21000 and time invested by him is 1 year, i.e., 12 months. At the same time B invested Rs. 36000 and time invested by him is x. So, if we equate their contributions, we get
$21000\times 12=36000\times x$
$\Rightarrow \dfrac{21000\times 12}{36000}=x$
$\Rightarrow x=7$
So, B invested 7 months, i.e., 5 months less than A. So, we can say that B joined after 5 months of A started the business. Hence, the answer to the above question is option (c).

Note: If you find it difficult to understand, you can think 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.