Question

The ratio of efficiencies of A to B, B to C and C to D are 2 ∶ 3, 3 ∶ 4 and 2 ∶ 5 respectively. If A and C together can complete a work in 65 days, then in how many days B and D can finish the same work?
1. 10 days
2. 26 days 
3. 30 days 
4. 40 days

Answer 1

Correct Answer - Option 3 : 30 days 

Given:

Ratio of efficiencies,

A ∶ B = 2 ∶ 3

B ∶ C = 3 ∶ 4

C ∶ D = 2 ∶ 5

A and C together can complete a work in 65 days.

Formula used:

Total work = Number of person × Efficiency × Number of days

M1D1H1/W1 = M2D2H2/W2      (where M is number of men, D is number of days, H is number of hours and W is amount of work.)

Calculations:

Ratio of efficiencies,

A ∶ B = 2 ∶ 3

B ∶ C = 3 ∶ 4

C ∶ D = (2 ∶ 5) _{× 2} → 4 ∶ 10

⇒ A ∶ B ∶ C ∶ D = 2 ∶ 3 ∶ 4 ∶ 10

Let the number of days required by B and D to complete the work be 'x days'.

Let the total work be '1'.

According to question,
⇒ {(2 + 4) × 65}/1 = {(3 + 10) × x}/1

⇒ x = 30 days.

∴ The number of days required by B and D to complete the work is 30 days.