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Question:

Rudra can do a piece of work in 9 days, Pratap in $2 \frac{4}{7}$ days and Singh in 18 days. All begin to do it together but Rudra leaves after 1 day and Pratap 2 days before the completion of work. How long would the work last?

Explanation:

Rudra can do a piece of work in 9 days, Pratap in $\frac{18}{7}$ days and Singh in 18 days.

Let the work be completed in ‘n’ days.

∴ Rudra works for 1 day, Pratap for (n – 2) days and Singh for n days.

∴ $\frac{1}{9} + \frac{(n - 2)}{18 / 7} + \frac{(n)}{18}$ = 1

⇒ $\frac{8 n - 12}{18}$ = 1

n = $\frac{30}{8}$ days or $3 \frac{3}{4}$ days

Hence, option (d).

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