Question

Sita and Gita invested the same capital in a business. At the year-end they share the profit in the ratio $3:2$. If sita has invested her capital for the whole year, for how many months gita has invested her capital?

• A. $8months$
• B. $7months$
• C. $5months$
• D. $9months$

Answer 1

The correct option is A $8months$

Let their same capital be $X$.

and let gita invested his capital for $y$ months.

At the end of 1 year the profit ratio is $3:2$

For sita =$X\times 12$

For gita=$X\times y$

Total shares=$12+y$

Profit of sita=$\frac{12}{12+y}-\left(1\right)$

Profit of geeta=$\frac{y}{12+y}‘-\left(2\right)$

from eqs.(1) and (2) we have-

$\frac{\frac{12}{12+y}}{\frac{y}{12+y}}=\frac{3}{2}⟹\frac{12}{y}=\frac{3}{2}$

$⟹y=8$

Hence sita invested her capital for $8$ months.