Mehdi can complete a piece of work in 25 hours. Jahnavi is 50 percent more efficient than Mehdi. If they work together on the same work, in how many hours will they finish it?

Introduction / Context:
This time and work problem introduces an efficiency comparison between two workers. One worker is said to be 50 percent more efficient than the other. We are given the time taken by the less efficient person alone and are asked to compute the time required when both work together.

Given Data / Assumptions:

• Mehdi alone completes the work in 25 hours.
• Jahnavi is 50 percent more efficient than Mehdi.
• Both workers maintain constant efficiency and work rates.
• We need to find the time taken to complete the work when Mehdi and Jahnavi work together.

Concept / Approach:
If Jahnavi is 50 percent more efficient, it means her rate of working is 1.5 times Mehdi's rate. Since Mehdi's time for the full work is known, we can find his rate and then multiply by 1.5 to find Jahnavi's rate. The combined rate is the sum of the two rates, and the reciprocal of this combined rate gives the total time when they work together.

Step-by-Step Solution:
Step 1: Let total work be 1 unit.Step 2: Mehdi completes the work in 25 hours, so Mehdi's rate = 1 / 25 of the work per hour.Step 3: Jahnavi is 50 percent more efficient than Mehdi. That means her rate = 1.5 times Mehdi's rate.Step 4: Compute Jahnavi's rate = 1.5 * (1 / 25) = 3 / 50 of the work per hour.Step 5: Combined rate of Mehdi and Jahnavi = Mehdi's rate + Jahnavi's rate = 1 / 25 + 3 / 50.Step 6: Convert to common denominator 50: 1 / 25 = 2 / 50, so combined rate = 2 / 50 + 3 / 50 = 5 / 50 = 1 / 10 of the work per hour.Step 7: Time taken when both work together = 1 divided by combined rate = 1 / (1 / 10) = 10 hours.

Verification / Alternative check:
To verify, in 10 hours Mehdi completes 10 * (1 / 25) = 10 / 25 = 2 / 5 of the work. In the same 10 hours, Jahnavi completes 10 * (3 / 50) = 30 / 50 = 3 / 5 of the work. The total completed work is 2 / 5 + 3 / 5 = 1 full job, confirming that 10 hours is correct when both work together.

Why Other Options Are Wrong:

• 12 hours: In 12 hours their total work would exceed 1, making this time too long relative to their combined rate.
• 3 hours: This is far too short for the work rates given and would require a much higher combined rate than 1 / 10.
• 9 hours: Their combined rate applied for 9 hours would produce only 9 / 10 of the work, not the full job.

Common Pitfalls:
Students sometimes misinterpret 50 percent more efficient as 50 percent of Mehdi's rate instead of 150 percent. The correct multiplier for 50 percent more is 1.5, not 0.5. Another pitfall is adding the times instead of the rates, which is incorrect. Always work with rates when multiple workers are involved simultaneously.

Final Answer:
Mehdi and Jahnavi together can complete the work in 10 hours.