Question

Vijay can do a piece of work in 4 hours. Ajay can do it in 28 hours. With the assistance of Amit, they completed the work in 3 hours. In how many hours can Amit alone do it?

• A. 23
• B. 20
• C. 21
• D. 22

Answer 1

Answer:

C. 21

Amit alone can do the work in 21 hours.

Let's assume the total work is the Least Common Multiple (LCM) of the given times (4, 28, and 3), which is 84 units.

1. Calculate individual efficiencies (work per hour):

   • Vijay's efficiency = $84 \div 4$ = 21 units/hour

   • Ajay's efficiency = $84 \div 28$ = 3 units/hour

   • Combined efficiency (Vijay + Ajay + Amit) = $84 \div 3$ = 28 units/hour

2. Find Amit's efficiency:

   • Amit's efficiency = Combined efficiency − (Vijay's + Ajay's efficiency)

   • Amit's efficiency = $28 - (21 + 3) = 28 - 24 =$ 4 units/hour

3. Calculate time taken by Amit alone:

   • $\text{Time} = \frac{\text{Total Work}}{\text{Amit's Efficiency}} = \frac{84}{4} =$ 21 hours