Ketan can do a piece of work in 9 hours. Mahesh can do it in 42 hours. With the help of David, they complete the work in 6 hours. In how many hours can David alone do the same piece of work three times?

Question

Question

This question was previously asked in

Punjab Police Constable Official Paper-I & II (Held On: 08 Aug, 2024 Shift 1)

Answer 1

Given:

Ketan can do the work in 9 hours.

Mahesh can do the work in 42 hours.

With the help of David, they complete the work in 6 hours.

Formula used:

Rate of work = 1 / Time

Calculation:

Rate of Ketan = 1 / 9

Rate of Mahesh = 1 / 42

Rate of David = 1 / x

The total rate of work done by Ketan, Mahesh, and David together is 1 / 6 (since they complete the work in 6 hours):

LCM of 9, 42, and 6 = 126

Now, multiply the entire equation by 126 to eliminate the denominators:

126 × (1/9 + 1/42 + 1/x) = 126 × (1/6)

⇒ 14 + 3 + 126/x = 21

⇒ 17 + 126/x = 21

⇒ 126/x = 4

⇒ x = 126 / 4 = 31.5

Therefore, David alone can complete the work in 31.5 hours.

Now, to find how many hours David will take to do the work three times:

Time for three times the work = 31.5 × 3 = 94.5 hours

∴ David alone will take 94.5 hours to complete the work three times.