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A and B together can do a piece of work in 60 days. B and C together can do the work in 40 days. A starts the work and works on it for 16 days then leaves. Then B takes up, works for 28 days, and leaves. Finally, C finishes the remaining work in 38 days. In how many days can B complete the entire work alone? 

A and B together can do a piece of work in 60 days. B and C together can do the work in 40 days. A starts the work and works on it for 16 days then leaves. Then B takes up, works for 28 days, and leaves. Finally, C finishes the remaining work in 38 days. In how many days can B complete the entire work alone?  Correct Answer 120 days

Given:

A and B together can do a piece of work = 60 days

B and C together can do a piece of work = 40 days

Concept Used:

Efficiency = Time taken × Work done

Calculation:

Let the total work be 120 (LCM of 60 ,40)

Let the efficiency of C be x

According to the question, we have

The efficiency of (A + B) = 120/60 ⇒ 2

The efficiency of (B + C) = 120/40 ⇒ 3

Now, A work for 16 days and B work for 28 days

Let assume A and B work together be 16 days

Let assume B and C work together be 12 days

Let assume C work alone be 26 days

According to the question,

(A + B) × 16 + (B + C) × 12 + C × 26 = 120

⇒ 2 × 16 + 3 × 12 + x × 26 = 120

⇒ 32 + 36 + 26x = 120

⇒ 26x = 120 - 68

⇒ 26x = 52

⇒ x = 2

The efficiency of B = The efficiency of (B + C) - The efficiency of C

The efficiency of B = 3 - 2 ⇒ 1

Now,

B can complete the entire work alone = (Total work)/(Efficiency of B)

⇒ 120/1 ⇒ 120 days

∴ The B can complete the entire work alone in 120 days.

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