Question

$A$ began a business with Rs. $\mathrm{85,000}$. He was joined afterwards by $B$ with Rs. $\mathrm{51,000}$. 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. $4$ months
• B. $6$ months
• C. $8$ months
• D. $3$ months

Answer 1

Answer: (A)

$4$ months

$Concept:$ Ratio of product of investment and time duration is equal to ratio of profit.

Here, For A, Investment (Contribution) $=85000$ Rs. for 1 year (12 months)

For B, investment $=51000$ Rs.

Let B joined A for $X$ months period.

Ratio of profit $=5:1$

Now, $\frac{InvestmentbyA\times Timedurationofinvestment}{InvestmentbyB\times Timedurationofinvestment}=Ratioofprofit$

$\Rightarrow \frac{85000\times 12}{51000\times X}=\frac{5}{1}$

$\Rightarrow X=\frac{85000\times 12}{51000\times 5}=4Months$

Hence, B joined A after $12-X=12-4=8$ months from start of business and hence he joined for $4$ months.