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Sunder, Ramu, and Chhotu can dig a well in 9, 18 and 36 days respectively. They all started digging together. Sunder worked continuously till well dug completely, Ramu leaves the work 3 days before its completion and Chhotu leaves the work 2 days before its completion. What is the time taken to dig the well? 

Sunder, Ramu, and Chhotu can dig a well in 9, 18 and 36 days respectively. They all started digging together. Sunder worked continuously till well dug completely, Ramu leaves the work 3 days before its completion and Chhotu leaves the work 2 days before its completion. What is the time taken to dig the well?  Correct Answer 44/7 days 

Given

Sunder, Ramu, and Chhotu can dig a well respectively in = 9, 18 and 36 days

Formula used

Rate of Work = 1/Time Taken

Calculation

Let the well dug completely in days = x days

Work done by Sunder in 1 day = 1/9

Work done by Ramu in 1 day = 1/18

Work done by Chhotu in 1 day = 1/36

So According to question,

x/9 + (x-3)/18 + (x-2)/36 = 1

⇒ (4x + 2x - 6 + x - 2)/36 = 1

⇒ (7x - 8)36 = 1

⇒ 7x - 8 = 36

⇒ 7x = 36 + 8 

⇒ x = 44/7

∴ Time taken to dig the well completely is 44/7 days.

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