Question

A, B and C together can build a wall in 12 days. C is four times as productive as B and A alone can build the wall in 48 days. In how many days A and B working together can build the wall?

• A. 20
• B. 30
• C. 80
• D. 40

Answer 1

Answer:

B. 30

Solution: Given : A, B and C can build a wall in 12 days C is 4 times as efficient as B and A alone can build that wall in 48 days Calculations : Total work = LCM of 12 and 48 ⇒ 48 units A's per day work = 48/48 = 1 units A, B and C per day work = 48/12 = 4 units B and C per day work = 4 - 1 = 3 units C is 4 times as efficient as B (given) Let C per day work be '4x' units and B per day work be 'x' unit So, 4x + x = 3 units 5x = 3 x = 3/5 unit B's per day work = x = 3/5 unit Now A and B per day work = 1 + (3/5) = 8/5 units Total days taken by A and B = 48/(8/5) ⇒ (48/8) × 5 ⇒ 30 days ∴ A and B will complete the work in 30 days