A and B can complete a piece of work in 15 days. B and C in 30 days and C and A in 45 days. In how many days will they complete the work if they start working together?

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Question

This question was previously asked in

SSC CHSL Exam 2024 Tier-I Official Paper (Held On: 04 Jul, 2024 Shift 1)

Answer 1

Given:

A and B can complete a piece of work in 15 days.

B and C can complete a piece of work in 30 days.

C and A can complete a piece of work in 45 days.

Formula Used:

Work rate of A + B + C = 1/(Work rate of A and B) + 1/(Work rate of B and C) + 1/(Work rate of C and A)

Time taken when A, B, and C work together = 1 / (Work rate of A + B + C)

Calculation:

Let the work rates of A, B, and C be A, B, and C respectively.

A + B = 1/15

B + C = 1/30

C + A = 1/45

Adding these three equations:

(A + B) + (B + C) + (C + A) = 1/15 + 1/30 + 1/45

⇒ 2A + 2B + 2C = 1/15 + 1/30 + 1/45

⇒ 2(A + B + C) = (6 + 3 + 2) / 90

⇒ 2(A + B + C) = 11 / 90

⇒ A + B + C = 11 / 180

Time taken when A, B, and C work together = 1 / (A + B + C)

⇒ Time = 1 / (11 / 180)

⇒ Time = 180 / 11

⇒ Time = 16 (4/11) days

The correct answer is option 2.

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