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Anuj finishes a work in 7 days when he works at double his efficiency. Charith finishes a work in 18 days when he works at triple his efficiency. Find the time taken by Birbal to finish the work alone if Anuj, Birbal and Charith together can finish it in 189/20 days.

Anuj finishes a work in 7 days when he works at double his efficiency. Charith finishes a work in 18 days when he works at triple his efficiency. Find the time taken by Birbal to finish the work alone if Anuj, Birbal and Charith together can finish it in 189/20 days. Correct Answer 63

Given:

Anuj finishes a work in 7 days when he works at double his efficiency. Charith finishes a work in 18 days when he works at triple his efficiency.

Formula used:

If A, B and C can finish a work in ‘a’, ‘b’ and ‘c’ days respectively and takes ‘t’ days together to finish the work, then, 1/t = 1/a + 1/b + 1/c

Calculation:

⇒ Anuj finishes a work in 7 days when he works at double his efficiency.

Hence, he normally takes 14 days to finish the work.

⇒ Charith finishes a work in 18 days when he works at triple his efficiency

Hence, he normally takes 54 days to finish the work.

Let the number of days Birbal takes to finish the work be ‘b’.

⇒ 1/14 + 1/b + 1/54 = 20/189

⇒ 1/b = 20/189 – 1/14 – 1/54 = 1/63

∴ number of days taken by Birbal to finish the work alone = 63 days

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