Question

A is 10% more efficient than B and B is 20% more efficient than C. While working together they can finish the work in 12 days. Find in how many days B can finish the work?
1. 40 days
2. \(35\frac15\) days
3. 30 days
4. \(25\frac13\) days

Answer 1

Correct Answer - Option 2 : \(35\frac15\) days

Given:

The efficiency of A = 110% × B

The efficiency of B = 120% × C

Time taken by (A + B + C) to complete the work = 12 days

Concept:

Efficiency × Total days taken to complete work = Total work

Calculation:

Efficiency of A = 110% × B

⇒ A/B = 11/10    ------(1)

Efficiency of B = 120% × C

⇒ B/C = 12/10 = 6/5      ------(2)

From (1) and (2;

Ratio of Efficiency of A, B and C = 33 ∶ 30 ∶ 25

Efficiency of (A + B + C) = (33a + 30a + 25a) = 88a

⇒ Total work done by A, B, C = (88a) × 12 = 1056a units      ------(3)

No of days taken by B to complete the work

= [1056a]/30a = \(35\frac15\) days

∴ B will take \(35\frac15\) days to complete the task.