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Explanation:

A invested for 1 year i.e., 12 months.
Let the time invested by B is x months.

We know that ratio of profit = ratio of (investment × time)

$\frac{\mathrm{Profit} \mathrm{of} \mathrm{A}}{\mathrm{Profit} \mathrm{of} \mathrm{B}}$ = $\frac{{\mathrm{I}}_{\mathrm{A}}\times {\mathrm{T}}_{\mathrm{A}}}{{\mathrm{I}}_{\mathrm{B}}\times {\mathrm{T}}_{\mathrm{B}}}$

⇒ $\frac{1}{1}$ = $\frac{25000\times 12}{40000\times \mathrm{x}}$

⇒ 40000x = 25000 × 12

⇒ 8x = 5 × 12

⇒ x = 60/8 = 7.5

∴ B invested after 12 - 7.5 = 4.5 months.

Hence, option (c).