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A and B complete a work in 2 days. If A alone can do it in 4 days then, B alone can do 17-times of the same work in ________(days).
Question

A and B complete a work in 2 days. If A alone can do it in 4 days then, B alone can do 17-times of the same work in ________(days).

A.

4

B.

68

C.

5

D.

69

Correct option is B

Given:

A and B together complete the work in 2 days

A alone completes it in 4 days

We need to find in how many days B alone can do 17 times the same work

Solution:

A's 1-day work = 14\frac{1}{4}​​

A + B’s 1-day work = 12\frac{1}{2}​​

B's 1-day work = 1214=14\frac{1}{2} - \frac{1}{4} = \frac{1}{4}​​

So, B can do the full work in 4 days

Now, for 17 times the work:

Time = 17 × 4 = 68 days

Alternate Solution:

Let total work = LCM of 2 and 4 = 4 units

A’s 1-day work = 44 \frac{4}{4}​ = 1 unit/day

A + B’s 1-day work = 42\frac{4}{2}​ = 2 units/day

B’s 1-day work = 2 − 1 = 1 unit/day

So B completes 4 units in 4 days

For 17 × 4 = 68 units, time = 681 \frac{68}{1}​ = 68 days

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