Benny can do a piece of work in 24 days. Chethan and David can do the same work individually in 36 and 48 days, respectively. All of them begin the work together. However, Benny leaves the work 4 days before the completion of work and Chethan leaves the work 10 days before the completion of the work. David worked till the end and completed the work. Find the number of days in which the work was completed.

Question

Question

This question was previously asked in

SSC CGL 2023 Tier-I Official Paper (Held On: 27 Jul 2023 Shift 2)

Answer 1

Shortcut Trick

Let x be the total time to complete the work,

B(x - 4) + C(x - 10) + D x = 144

⇒ 6(x - 4) + 4(x - 10) + 3x = 144

⇒ 6x - 24 + 4x - 40 + 3x = 144

⇒ 13x = 144 + 40 + 24

⇒ x = 208/13 = 16

Thus, time taken to complete the work = x = 16 days

Alternate Method

Given:

The Benny can do a piece of work = 24 days

The Chethan can do a piece of work = 36 days

The David can do a piece of work = 48 days

Formula used:

Work = Efficiency × Time

Calculation:
Let the work was complete in X days.

One day work of Benny = \({1\over24}\)

One day work of Chethan = \({1\over36}\)

One day work of David = \({1\over48}\)

According to the question

⇒ \({{X-4\over24}+{X-10\over36}+{X\over 48}}=1\)

⇒ \({{6\ × (X-4)}+{4× (X-10)+3X}\over144}=1\)

⇒ 6X - 24 + 4X - 40 + 3X = 144

⇒ 13X - 64 = 144

⇒ 13X = 208

⇒ X = 16

∴ The required result will be 16.

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