Mitu can do a piece of work in 12 hours, Titu and Situ together in 2 hours, and Mitu and Situ together in 3 hours. How long will Titu alone take to do it?

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Question

This question was previously asked in

SSC CPO 2024 Official Paper-I (Held On: 27 Jun, 2024 Shift 3)

Answer 1

Given:

Mitu's time to complete the work = 12 hours

Titu and Situ's time together = 2 hours

Mitu and Situ's time together = 3 hours

Formula used:

Work done per hour = 1 / Time taken

If A and B work together, their combined work per hour = Work done by A + Work done by B

Calculations:

Let Titu's time to complete the work = T hours

Let Situ's time to complete the work = S hours

Mitu's work per hour = 1/12

Titu and Situ's combined work per hour = 1/2

Mitu and Situ's combined work per hour = 1/3

Situ's work per hour:

⇒ 1/S = 1/3 - 1/12

⇒ 1/S = 4/12 - 1/12 = 3/12 = 1/4

⇒ S = 4 hours

Titu's work per hour:

⇒ 1/T + 1/4 = 1/2

⇒ 1/T = 1/2 - 1/4

⇒ 1/T = 2/4 - 1/4 = 1/4

⇒ T = 4 hours

∴ Titu alone will take 4 hours to complete the work.