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A is twice as good a workman as B and together they finish a piece of work in 13 days. In how many days will B alone finish the work?
1. 19.5
2. 39
3. 21
4. 42

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Correct Answer - Option 2 : 39

Given:

A is twice as good a workman as B and together they finish a piece of work in 13 days.

Concept Used:

Efficiency ∝ 1/Time

Calculation:

The efficiency ratio of A and B is 2 : 1

The time ratio of A and B is 1 : 2

Let, A took time x days and B took time 2x days to complete the work alone

In 1 day A can do 1/x part of the work

In 1 day B can do 1/2x part of the work

Together in 1 day they can do 1/13 part of the work

(1/x) + (1/2x) = 1/13

⇒ 3/2x = 1/13

⇒ x = 39/2

B alone will finish the work in 2 × (39/2)

= 39 days

∴ In 39 days B alone will finish the work.

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