Question

Three friends — Asit, Arnold and Afzal — work together to get chores done. Time together is 6 hr less than Asit alone, 1 hr less than Arnold alone, and half the time Afzal alone would take. How long did it take them together?

• A. 20 min
• B. 30 min
• C. 40 min
• D. 50 min

Hint:

In combined work problems, express each person’s rate as reciprocal of time, then sum and solve.

Answer 1

The Correct Option is C

Let $T$ = time together in hours. Asit = $T+6$, Arnold = $T+1$, Afzal = $2T$. Work rates: $\frac1{T+6} + \frac1{T+1} + \frac1{2T} = \frac1{T}$. Multiply through by $2T(T+6)(T+1)$ and solve: $2T(T+1) + 2T(T+6) + (T+6)(T+1) = 2(T+6)(T+1)$. Simplifying gives $T= \frac23$ hr = 40 min.