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 ?

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,
$$\eqalign{ & \Leftrightarrow \frac{{{{\text{C}}_1} \times {{\text{T}}_1}}}{{{{\text{C}}_2} \times {{\text{T}}_2}}} = \frac{{{{\text{P}}_1}}}{{{{\text{P}}_2}}} \cr & \Leftrightarrow \frac{{11x \times 8}}{{12x \times {{\text{T}}_2}}} = \frac{2}{3} \cr & \Leftrightarrow {{\text{T}}_2} = 11{\text{ months}} \cr} $$
Hence the time for which Y invested his capital is 11 months