Question

33. A is twice as efficient as B and B is twice as efficient as C. All three working together with D can complete a work in 4 days. If D alone can do this work in 16 days, in how many days will A alone do 75% of the same work ? (2) 8 (3) 7 (4) 9 (1) 6.​

Answer 1

Answer:

A works twice as fast as B and B works twice as fast as C

Let efficiency of C = 1 unit

Efficiency of B = 2 units

Efficiency of A = 4 units

Given that D alone can finish the same task in 16 days.

As total work is 100%

So work done by D in 4 days = 25%

It is also given that all three working together can finish total task in 4 days with the help of D

So work done by (A+B+C) in 4 days = 100% - 25% = 75%

Efficiency of (A+B+C) = 1+2+4 = 7 units

So work done by (A+B+C) in 4 days = 7 x 4 units

⇒ 7 x 4 units = 75% of total work……………….(1)

Now we will find that in how many days will A alone finish 75% of the same task.

Efficiency of A = 4 units

Let A will finish 75% of the same task in x days.

So, 4x units = 75% of total work ……………..(2)

Compare (1) and (2)

x = 7 days

So, 7 will be the answer.