Question

Rishi can do a piece of work in 8 hours. Shan can do it in 12 hours. With the assistance of Veer, they completed the work in 3 hours. In how many hours can Veer alone do it?

• A. 8
• B. 9
• C. 7
• D. 10

Answer 1

Answer:

A. 8

Veer alone can complete the work in 8 hours.

To make this easy to solve without fractions, let’s find a total amount of work using the LCM (Least Common Multiple) of the given hours (8, 12, and 3).

• Let the Total Work = 24 units (LCM of 8, 12, and 3).

Step 1: Find the work done by each per hour (Efficiency)

• Rishi's efficiency: 24 units / 8 hours = 3 units/hour

• Shan's efficiency: 24 units / 12 hours = 2 units/hour

• Combined efficiency (Rishi + Shan + Veer): 24 units / 3 hours = 8 units/hour

Step 2: Find Veer's efficiency

• Rishi and Shan together do: 3 + 2 =5 units/hour

• Veer's work per hour = Combined efficiency - (Rishi + Shan)

• Veer's efficiency = 8 - 5 = 3units/hour

Step 3: Calculate the time taken by Veer alone

• Time = Total Work / Veer's Efficiency

• Time = 24 / 3 = 8 hours