Question

A, B, C, and D can do a piece of work in 20 days. If A and B can do it together in 50 days, and C alone in 60 days, find the time in which D alone can do it.

1. 120 days

2. 200 days

3. 150 days

4. 90 days

5. 75 days

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Answer 1

Answer: 75 days

Step-by-step explanation:

• Given,A,B,C and D can do a work in 20 days.
• Also A and B can do the same work in 50 days.
• C can do it alone in 60 days.
• Let that D can do that work in x days.
• Now, according to question

        $\frac{1}{50}+\frac{1}{60}+\frac{1}{x}=\frac{1}{20}$

   ⇒$\frac{6+5}{300}+\frac{1}{x}=\frac{1}{20}$

  ⇒$\frac{1}{x}=\frac{1}{20}-\frac{11}{300}$

  ⇒$\frac{1}{x}=\frac{15-11}{300}$

  ⇒$\frac{1}{x}=\frac{4}{300}$

  ⇒x=$\frac{300}{4}$

  ∴ x=75 days.

• Hence,D can do the work alone in 75 days.