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Question:

A and B together can finish a job in 40 days. A can do the same job on her own in 60 days. How long will B take to do the three-fourth of the same work all alone?

Explanation:

Let the total work to be done = LCM(40, 60) = 120 units.

Efficiency of A alone = 120/60 = 2 units/day

Efficiency of A and B together = 120/40 = 3 units/day

∴ Efficiency of B alone = 3 - 2 = 1 unit/day

⇒ Time taken by B alone to complete the work = 120/1 = 120 days.

⇒ Time taken by B alone to complete 3/4th work = 120 × 3/4 = 90 days.

Alternately,
Let B taken B days to complete the work alone.

⇒ $\frac{1}{40}$ = $\frac{1}{60}$ + $\frac{1}{\mathrm{B}}$

⇒ $\frac{1}{40}$ - $\frac{1}{60}$ = $\frac{1}{\mathrm{B}}$

⇒ $\frac{1}{\mathrm{B}}$ = $\frac{3-2}{120}$

⇒ B = 120

⇒ Time taken by B alone to complete 3/4th work = 120 × 3/4 = 90 days.

Hence, option (c).