Question

A alone can complete the work in 12 days and B alone can complete the work in 24 days. When A, B and C worked together then work will be completed in 72/11 days. In how many days C alone can complete the half of the work?
1. 18 days
2. 72 days
3. 36 days
4. 40 days

Answer 1

Correct Answer - Option 1 : 18 days

Given:

A can do the work in 12 days

B can do the work in 24 days

A, B, C can do the work in 72/11 days

Calculation:

A's 1 days work = 1/12

B's 1 days work = 1/24

⇒ (A + B + C)'s 1 days work = 1/12 + 1/24 + 1/C

⇒ 1/12 + 1/24 + 1/C = 11/72

⇒ 1/C = 1/36

C alone can complete the work in 36 days.

∴ Time taken by C to complete half of work = 36 × 1/2 = 18 days

Time taken by a person to complete a/b fraction of work = a/b × (Number of days in which person alone can complete work)