A and B together can complete a work in 12 days. B and C together can complete the same work in 15 days. C and A together can do…

Question

A and B together can complete a work in 12 days. B and C together can complete the same work in 15 days. C and A together can do it in 20 days. In how many days can A alone complete the job?

1. A. 30 days (Correct answer)
2. B. 20 days
3. C. 50 days
4. D. 15 days

Correct Answer

Option A — 30 days

Detailed Solution & Explanation

The correct answer is 30 days.

Key Points

• Convert each pair into one day's work:
  • A + B = 1/12, B + C = 1/15, C + A = 1/20
• Add all three: 2(A + B + C) = 1/12 + 1/15 + 1/20 = (5 + 4 + 3)/60 = 12/60 = 1/5.
• So A + B + C = 1/10 of the work per day.
• A alone = (A + B + C) − (B + C) = 1/10 − 1/15 = (3 − 2)/30 = 1/30.
• A therefore takes 30 days.

Additional Information

• The standard trick in pairwise work questions is to add all the pairs, which counts every worker twice and yields the combined rate in one step.
• To isolate any individual, subtract the pair that excludes them from the combined rate.
• Taking the LCM of 12, 15 and 20 as total work (60 units) gives the same result with whole numbers: A+B = 5, B+C = 4, C+A = 3 units/day, total = 6, so A = 6 − 4 = 2 units/day → 60/2 = 30 days.

प्रश्न (हिन्दी में)

A और B मिलकर एक काम को 12 दिनों में पूरा कर सकते हैं। B और C मिलकर उसी काम को 15 दिनों में पूरा कर सकते हैं। C और A मिलकर उसी काम को 20 दिनों में पूरा कर सकते हैं। A अकेले उस काम को कितने दिनों में पूरा कर सकता है?

1. A. 30 दिन
2. B. 20 दिन
3. C. 50 दिन
4. D. 15 दिन