Question

A and B together can finish a work in 16 days, while B can do the same work alone in 24 days. In how many days can A alone finish the work ?

• A. 25 days
• B. 20 days
• C. 48 days
• D. 42 days

Answer 1

Answer:

C. 48 days

A alone can finish the work in 48 days.

Method 1: Shortcut Formula
When the combined time of two people (X) and the individual time of one person (Y) are given, the formula for the other person's time is:
$\text{Days taken by A} = \frac{X \times Y}{Y - X}$

• Combined time (A + B) = 16 days

• B's individual time = 24 days

$\text{Days taken by A} = \frac{16 \times 24}{24 - 16} = \frac{384}{8} = \mathbf{48\text{ days}}$

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Method 2: LCM (Total Work) Method

1. Find the LCM of 16 and 24 to assume the Total Work.

   • LCM(16, 24) = 48 units (Total Work)

2. Find their daily work efficiency:

   • Efficiency of (A + B) = $\frac{48}{16}$ = 3 units/day

   • Efficiency of B = $\frac{48}{24}$ = 2 units/day

3. Find A's individual efficiency:

   • A's efficiency = (A + B) - B = 3 - 2 = 1 unit/day

4. Calculate days for A:

   • Days = $\frac{\text{Total Work}}{\text{A's efficiency}} = \frac{48}{1} = \mathbf{48\text{ days}}$