Question

A can finish \(\frac{2}{5}\) of a task in 12 days and B can finish\(\frac{2}{3}\) of the same task in 30 days. They work together for 10 days. C alone complete the remaining task in 16 days, B and C together will complete \(\frac{4}{5}\) of the same task in:
1. 16 days
2. 12 days
3. 20 days
4. 15 days

Answer 1

Correct Answer - Option 1 : 16 days

Given:

A can finish \(\frac{2}{5}\) of a task in 12 days and B can finish\(\frac{2}{3}\) of the same task in 30 days.

Calculation:

A's 1 day's work = 2/5 × 1/12 = 1/30

B's 1 day's work = 2/3 × 1/30 = 1/45

(A + B)'s 1 days work = 1/30 + 1/45 = 1/18

(A + B)'s 10 days work = 10 × 1/18 = 5/9

Remaining work = 1 - 5/9 = 4/9

C's 1 day's work = 4/9 × 1/16 = 1/36

(B + C)'s 1 day's work = 1/45 + 1/36 = 9/180 = 1/20

∴ B and C will complete 4/5th work in = 4/5 × 20 = 16 days.

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