The ratio of the efficiencies of two workers, P and Q, is 5 : 2. If P can complete a project in 12 days, how many days will Q tak…

Question

The ratio of the efficiencies of two workers, P and Q, is 5 : 2. If P can complete a project in 12 days, how many days will Q take to complete the same project alone?

1. A. 24 days
2. B. 30 days (Correct answer)
3. C. 35 days
4. D. 40 days

Correct Answer

Option B — 30 days

Detailed Solution & Explanation

The correct answer is 30 days.

Key Points

• Efficiency and time are inversely proportional: the more efficient worker takes proportionally less time.
• With efficiencies in $5 : 2$, the times are in $2 : 5$.
• P takes 12 days, so Q takes $12 \times \tfrac{5}{2} = $ 30 days.

Additional Information

• The inversion is the whole question. Multiplying 12 by 5/2 rather than 2/5 is the intended error, and it gives 4.8 days — obviously wrong, since Q is the slower worker.
• A sanity check that costs nothing: Q is less efficient, so Q's time must exceed 12 days.
• Working together they would finish in $\dfrac{12 \times 30}{12 + 30} = \tfrac{360}{42} \approx 8.57$ days.

प्रश्न (हिन्दी में)

दो श्रमिकों, P और Q की कार्यक्षमता का अनुपात 5 : 2 है। यदि P एक परियोजना को 12 दिनों में पूरा कर सकता है, तो Q को अकेले उसी परियोजना को पूरा करने में कितने दिन लगेंगे?

1. A. 24 दिन
2. B. 30 दिन
3. C. 35 दिन
4. D. 40 दिन