The ratio of investments of two partners X and Y is 11 : 12 and the ratio of their profit is 2 : 3. If X invested the money for 8 months, then the time for which Y invested the money is ?

Answer: Option D

Let capital of X be Rs. 11x and Y's capital be Rs. 12x
and let time for which Y invested capital is T₂ months
by using formula,
$$\begin{array}{rl}& \iff \frac{{\text{C}}_1\times {\text{T}}_1}{{\text{C}}_2\times {\text{T}}_2}=\frac{{\text{P}}_1}{{\text{P}}_2}\\ & \iff \frac{11x\times 8}{12x\times {\text{T}}_2}=\frac{2}{3}\\ & \iff {\text{T}}_2=11\text{ months}\end{array}$$
Hence the time for which Y invested his capital is 11 months