The ratio of efficiencies of A and B to do a certain work is 5:2. A takes *X* hours to complete the work, and C destroys the work in *X + 5* hours. All three start working at 7 a.m. and finish at 1 p.m. C works only for the duration A works. Find the time taken by C alone to completely destroy the finished work.

Statement (I): A can complete $ $\frac{8}{9}$ $ of the work in 16 hours.

Statement (II): The efficiency ratio of B to C is 5:1.

Which of the following is true?

Question

The ratio of efficiencies of A and B to do a certain work is 5:2. A takes *X* hours to complete the work, and C destroys the work in *X + 5* hours. All three start working at 7 a.m. and finish at 1 p.m. C works only for the duration A works. Find the time taken by C alone to completely destroy the finished work.

Statement (I): A can complete $ $\frac{8}{9}$ $ of the work in 16 hours.

Statement (II): The efficiency ratio of B to C is 5:1.

Which of the following is true?

Accepted Answer

**Solution:**

1. Given the efficiency ratio of A to B is 5:2 and A takes *X* hours to complete the work.

2. Statement (I) says A can complete $ $\frac{8}{9}$ $ of the work in 16 hours.
   - From this, time taken by A to complete the whole work = $ $\frac{16 \times 9}{8} = 18 $$ hours.
   - So, *X* = 18 hours.

3. Since C destroys the work in *X + 5* hours, C takes $ 18 + 5 = 23 $ hours to destroy the work.

4. All three start at 7 a.m. and finish at 1 p.m., so total time = 6 hours.

5. C works only for the time A works, which is 6 hours.

6. Using the above, we can find the time taken by C to destroy the work completely, which is 23 hours.

7. Statement (II) gives the efficiency ratio of B to C as 5:1, but without knowing *X* or actual time taken by A, this alone is insufficient.

**Answer:** (e) Statement (I) alone is sufficient but statement (II) alone is not sufficient.

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