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A, B, C and D are four workers, working together they can finish a job in 24 days. A is twice efficient than B, C is thrice efficient than B and D is twice efficient than C. Amount of Rs.480 is their total daily wage. In how many days D alone can do the work, also what is the daily wage of D.

A, B, C and D are four workers, working together they can finish a job in 24 days. A is twice efficient than B, C is thrice efficient than B and D is twice efficient than C. Amount of Rs.480 is their total daily wage. In how many days D alone can do the work, also what is the daily wage of D. Correct Answer 48, 240

Given :

Total time taken to complete the wok = 24 days

Concept used :

Let time taken by two person’s A and B to do a certain work is ‘A’ days and ‘B’ days respectively, then time taken by both of them together to do that work which is ‘T’ days can be calculated by formula :

(1/A) + (1/B) = 1/T

Calculations :

Let A’s one day work be 1/A

Then B’s one day work = 1/B

C’s one day works = 1/C

D’s one day work = 1/D

Total time taken by them is 24 days

∴ (1/A) + (1/B) + (1/C) + (1/D) = 1/24     ----(i)

A is twice efficient than B

⇒ 1/A = 2/B

C is thrice efficient than B

⇒ 1/C = 3/B

D is twice efficient of C

⇒ 1/D = 2/C = 6/B

∴ Equation (i) becomes

⇒ (2/B) + (1/B) + (3/B) + (6/B) = 1/24

⇒ 12/B = 1/24

⇒ B = 288 days

∴ Time in which D can finish the work = 288/6 = 48

Time taken by A = 288/2 = 144

Time taken by C = 288/3 = 96

Ratio of daily wage of A ∶ B ∶ C ∶ D = 2 ∶ 1 ∶ 3 ∶ 6

∴ Daily wage of D = (6/12) × 480 = 240

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