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 .4 monthsB .6 monthsC .8 monthsD .3 months

HINT:Proceed the solution of this question, using the concept that ratio of product of investment and time duration is equal to ratio of profit.

Here, in question it is given, for A, Investment (Contribution) =85000 Rs. for 1 year (12 months)
For B, investment =51000 Rs.
Let B join A for X months’ period.

Now, we know that $\dfrac{{{\text{Investment by A}} \times {\text{ Its time duration of investment }}}}{{{\text{Investment by B}} \times {\text{ Its time duration of investment}}}} = {\text{ ratio of profit}}$

It is given ratio of their profit =5:1
⇒$\dfrac{{8500 \times {\text{ 12}}}}{{5100 \times {\text{ x}}}} = {\text{ }}\dfrac{5}{1}$
On doing cross multiplication
$\Rightarrow 8500 \times {\text{ 12}} = {\text{ }}5 \times 5100{\text{x}}$
On solving
$\Rightarrow \dfrac{{8500 \times {\text{ 12}}}}{{5 \times 5100}} = {\text{ x}}$
⇒x ​ = 4 Months
Hence, B joined A after 12−x=12−4=8 months from the start of business and hence he joined for 4 months.

Note-In this particular question, we have to find only the ratio of profit by A and B so here we can consider the profit as a product of investment and duration of investment by anyone. Here we have