Discussion

Explanation:

Unitary Method:

A’s 1 day’s work = $\frac{1}{10}$

B’s 1 day’s work = $\frac{1}{15}$

∴(A+B)'s 1 day' s work $\frac{1}{10}+\frac{1}{15}$ = $\frac{5}{30}$ = $\frac{1}{6}$

∴ Both together can finish the work in $\frac{1}{1/6}$ or 6 days

LCM Method:

Let the total work to be done = LCM(10, 15) = 30 units

A can complete this work in 10 days, hence A’s efficiency = 30/10 = 3 units/day

B can complete this work in 15 days, hence A’s efficiency = 30/15 = 2 units/day

Combined efficiencies of A and B = 3 + 2 = 5 units/day

Time taken by A and B together to complete the work = 30/5 = 6 days.

Hence, option (a).

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