Question

A can finish \(\frac 3 5\) of a task in 6 days and B can finish \(\frac 2 3\) of the same task in 12 days. A and B worked together for 5 days. C alone completed the remaining task in 8 days. B and C, working together, will complete the same task in:
1. 10 days
2. 18 days
3. 12 days
4. 15 days

Answer 1

Correct Answer - Option 3 : 12 days

Given:

A can finish \(\frac 3 5\) of a task  = 6 days 

B can finish \(\frac 2 3\) of the same task = 12 days

A and B worked together = 5 days

C alone completed the remaining task = 8 days

Concept Used:

If a man can do a work in t days then in 1 day he will do 1/t part of the work

Calculation:

A alone can finish task =  6 × (5/3)

⇒ 10 days

B alone can finish task = 12 × (3/2)

⇒18 days

⇒ A and B worked for 5 days = (5/10) + (5/18)

⇒ (45 + 25) /90 = 70/90

⇒ 7/9

⇒ Remaining work = 1 - (7/9)

⇒ 20/90 = 2/9

2/9^th  of work completed by C = 8 days

C alone can finish task =  8 × (9/2) = 36 days

⇒ B + C working together can do in 1 day = 1/18 + 1/36

⇒ (2 + 1)/36 = 3/36 = 1/12

In one day B and C together can complete  = 1/12 of the task

B and C together can complete a task = 12 day

∴ The number of days taken to complete a task B and C together is 12