Question

The ratio of the number of days required by Pramod and Vallabh to finish the work alone is 2 ∶ 3. It is also known that they take 6 days to complete the work together. Both worked together for the first three days, after which Pramod left. Find the number of days required by Vallabh to finish the remaining work alone.
1. 10
2. 7.5
3. 12.5
4. 13
5. 9

Answer 1

Correct Answer - Option 2 : 7.5

Given:

Ratio of the number of days required by Pramod and Vallabh to finish the work alone = 2 ∶ 3

Number of days required to complete the work together = 6

Number of days they worked together = 3

Formula Used:

If a person takes x days to complete a work alone, the part of the work he completes in 1 day = 1/x

Calculation:

Let the number of days required by Pramod to complete the work alone = 2x

So, the part of the work completed by Pramod in one day = 1/2x

Let the number of days required by Vallabh to complete the work alone = 3x

So, the part of the work completed by Vallabh in one day = 1/3x

Hence, when they work together for a day, the part of the work they complete is given by:

(1/2x) + (1/3x) = 1/6

⇒ x = 5

Hence, the number of days required by Pramod to complete the work alone = 2 × 5 = 10

Also, the number of days required by Vallabh to complete the work alone = 3 × 5 = 15

So, when they work together for 3 days, the part of the work completed = 3 × (1/6) = 1/2

So, the remaining work to be completed by Vallabh alone = 1- (1/2) = 1/2

Hence, the number of days required by Vallabh to finish the remaining work alone is given by:

15/2 = 7.5

∴ The number of days required by Vallabh to finish the remaining work alone is 7.5