Question

Gauri can complete a work in 3 hours and she is 2 times more efficient than Sita. How long will they take to finish a work 2 times as big if they work together on it?

• A. 4 hours
• B. 3.5 hours
• C. 2.5 hours
• D. 2 hours

Hint:

In time and work problems, always convert efficiency statements into work rates and adjust calculations when the size of work changes.

Answer 1

The Correct Option is A

Step 1: Determine Gauri’s work rate.
Gauri completes 1 work in 3 hours.
So, Gauri’s rate of work \( = \frac{1}{3} \) work per hour.
Step 2: Determine Sita’s work rate using efficiency relation.
Gauri is 2 times more efficient than Sita.
So, Sita’s efficiency (and work rate) is half of Gauri’s.
Sita’s rate of work \( = \frac{1}{6} \) work per hour.
Step 3: Calculate their combined work rate.
Combined rate of work \[ = \frac{1}{3} + \frac{1}{6} = \frac{1}{2} \] work per hour.
Step 4: Consider the size of work to be completed.
The work to be done is 2 times the original work.
So, total work \( = 2 \) units.
Step 5: Calculate the time required.
\[ \text{Time} = \frac{\text{Total work}}{\text{Combined rate}} = \frac{2}{\frac{1}{2}} = 4 \text{ hours} \]
Step 6: Conclusion.
If Gauri and Sita work together, they will complete the work in 4 hours.