Question

Guddu and Sonu can do a certain work in 12 days and 24 days respectively. They started the work together, but Sonu left after some time and Guddu finished the remaining work in 6 days. After how many days (from the start) did Sonu leave?

• A. 4 days
• B. 3 days
• C. 5 days
• D. 6 days

Hint:

When solving work problems, break the problem into smaller parts. Calculate the work done by each individual and then combine their work rates based on the time they work together.

Answer 1

The Correct Option is A

Let the total work be \( W \). Step 1: Work done by Guddu and Sonu.
- Guddu can complete the work in 12 days, so Guddu's work rate is \( \frac{1}{12} \) of the work per day.
- Sonu can complete the work in 24 days, so Sonu's work rate is \( \frac{1}{24} \) of the work per day. Step 2: Total work done when they both work together.
Let Sonu work for \( x \) days. In \( x \) days, the total work done by both Guddu and Sonu is: \[ \text{Work done by Sonu} = x \times \frac{1}{24} \] \[ \text{Work done by Guddu} = x \times \frac{1}{12} \] The total work done in \( x \) days is the sum of the work done by both: \[ \text{Total work done by both} = x \left( \frac{1}{24} + \frac{1}{12} \right) = x \left( \frac{1}{24} + \frac{2}{24} \right) = \frac{3x}{24} = \frac{x}{8} \] Step 3: Work done by Guddu after Sonu leaves.
After Sonu leaves, Guddu finishes the remaining work in 6 days. The remaining work is: \[ \text{Remaining work} = 1 - \frac{x}{8} \] Since Guddu works at a rate of \( \frac{1}{12} \) of the work per day, the work done by Guddu in 6 days is: \[ \text{Work done by Guddu in 6 days} = 6 \times \frac{1}{12} = \frac{1}{2} \] Step 4: Solve for \( x \).
The remaining work is \( \frac{1}{2} \), so we have the equation: \[ 1 - \frac{x}{8} = \frac{1}{2} \] Solving for \( x \): \[ \frac{x}{8} = \frac{1}{2} \] \[ x = 4 \] Step 5: Conclusion.
Sonu left after 4 days, which corresponds to option (1).