Question

A is thrice as fast as b, and is therefore able to finish a work in 60 days less than


b.find the time in which they can do it working together .

Answer 1

45/2 days will be the answer

Answer 2

Given:

A is thrice as fast as B

A is able to finish a work in 60 days less than B

To find:

The time in which A and B can complete the work together

Solution:

A is thrice as fast as B

∵ $Efficiency$ ∝ $\frac{1}{Time}$

So, if A takes "x" days to complete the work then B will take "3x" days.

Also, A completes the work in 60 days less than B, so we can form an equation as

3x - x = 60

⇒ 2x = 60

⇒ x = $\frac{60}{2}$

⇒ x = 30 days ← time taken by A to complete the work

∴ 3x = 3 × 30 = 90 days ← time taken by B to complete the work

So,

The amount of work done by A in 1 day = $\frac{1}{30}$

and

The amount of work done by B in 1 day = $\frac{1}{90}$

Now, we will find the time in which A & B can complete the work together:

The amount of work done by A & B together in 1 day is,

$= \frac{1}{90} \: + \: \frac{1}{30} \\\\\\taking\: L.C.M\: of \:the\: denominator\\\\\\= \frac{1\:+\:3}{90} \\\\\\= \frac{4}{90}$

Thus, the time in which both A and B can do the work together is $\frac{90}{4}$ days or 22.5 days.

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