Question

Amit and Varun can do a piece of work 1n 15 days. Varun alone can do 1/5 of the work in 5 days. In how many days Amit alone can do the whole work?
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Answer 1

Amit alone can do the whole work in 37.5 days.

• Let the total work be taken as 1.

• Given that,

Amit and Varun can finish the work together in 15 days.

=> Work done by Amit and Varun together in 1 day = 1 / 15

• Let the number of days in which Varun alone can complete the work be x.

=> Work done by Varun alone in 1 day = 1 / x  -(i)

=> Work done by Varun alone in 5 days = 5 × (1 / x) = 5 / x

• Given that,

Varun does 1 / 5 of the work in 5 days.

Therefore, equating the work done by Varun in 5 days, we get,

5 / x = 1 / 5

On cross-multiplying, we get,

=> 5 × 5 = 1 × x

=> 25 = x

Or, x = 25

Therefore, Varun alone can do the whole work in 25 days.

• Putting the value of x in equation (i), we get,

Work done by Varun alone in 1 day = 1 / 25

• Now, let the number of days in which Amit alone can complete the whole work be y.

=> Work done by Amit alone in 1 day = 1 / y

• Now,

Work done by Amit and Varun together in 1 day = Work done by Amit alone in 1 day + Work done by Varun alone in 1 day

=> (1 / 15) = (1 / y) + (1 / 25)

=> (1 / 15) - (1 / 25) = 1 / y

L.C.M. of 15 and 25 = 75

=> [ {1 × (75 / 15)}  - {1 × (75 / 25)} ] / 75 = 1 / y

=> { (1 × 5) - (1 × 3) } / 75 = 1 / y

=> (5 - 3) / 75 = 1 / y

=> 2 / 75 = 1 / y

=> 1 / y = 2 / 75

=> y = 75 / 2

=> y = 37.5

Therefore, number of days in which Amit alone can complete the work = 37.5

Answer 2

37 whole no. 1/2

Step-by-step explanation:

15+5=20

1/5÷20

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