Question

If A, B, and C do a piece of work, A alone completes 3/4^th part of work in 9 days and the efficiency ratios of A, B and C is 2 ∶ 3 ∶ 4. If they work together, find the total time to complete the work?

1. \(2\frac{1}{3}\) days
2. \(2\frac{6}{9}\) days
3. \(3\frac{1}{3}\) days
4. \(3\frac{6}{9}\) days

Answer 1

Correct Answer - Option 2 : \(2\frac{6}{9}\) days

Given:

A completes 3/4^th part in 9 days

Efficiency ratio of A, B, and C = 2 ∶ 3 ∶ 4

Concept used:

Time ratio = 1/Efficiency ratio

Total Time together to complete work = Work/1-Day work

Calculation:

Time to complete 3/4^th part of work by A = 9 days

⇒ Time to complete work by A = 9 × 4/3

⇒ Time to complete work by A = 12 days

Efficiency ratio of A, B, and C = 2 ∶ 3 ∶ 4

Time ratio = 1/Efficiency ratio

Total time ratio by A, B, and C = 1/2 ∶ 1/3 ∶ 1/4

⇒ Required ratio = 6 ∶ 4 ∶ 3

So, the total time to complete a work by A, B, and C is 6x days, 4x days, and 3x days respectively.

Time to complete work by A = 12 days

⇒ 6x = 12 days

⇒ x = 2 days

Time to complete work by B = 4x

⇒ Time to complete work by B = 8 days

Time to complete work by C = 3x

⇒ Time to complete work by C = 6 days

One day work of A = 1/12

One day work of B = 1/8

One day work of C = 1/6

A, B, and C together complete 1-day work = 1-day work of A + 1-day work of B + 1-day work of C

⇒ Required 1-day work = 1/12 + 1/8 + 1/6

⇒ Required 1-day work = (2 + 3 + 4)/24

⇒ Required 1-day work = 9/24

Total Time together to complete work = Work/1-Day work

⇒ Total Time together to complete work = 1/(9/24)

⇒ Total Time together to complete work = 24/9 days

∴ Total Time together to complete work is \(2\frac{6}{9}\) days.