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A builder appoints three construction workers Ramesh, Suresh and Kamlesh on one of his sites. They take 10, 15, and 30 days respectively to do a piece of work. How many days will it take Ramesh to complete the entire work if he is assisted by Suresh and Kamlesh every third day?

A builder appoints three construction workers Ramesh, Suresh and Kamlesh on one of his sites. They take 10, 15, and 30 days respectively to do a piece of work. How many days will it take Ramesh to complete the entire work if he is assisted by Suresh and Kamlesh every third day? Correct Answer 8 days

Given:

Ramesh, Suresh, and Kamlesh take 10, 15, and 30 days respectively.

Calculation:

Suppose the total work be the LCM of (10, 15, 30) be 30 unit

So, the efficiency of Ramesh = 30/10 = 3 units/day

Efficiency of Ramesh = 30/15 = 2 units/day

And, efficiency of Kamlesh = 30/30 = 1 unit/day

Work Done in 3 days (1 day of all three together + 2 days of Ramesh’s work) = 2 × 3 + (3 + 2 + 1) = 12 units

⇒ Work done in 3 days = 12 units

⇒ Wok done in 6 days= 24 units

And on 7th and 8th day Ramesh will work alone and perform total work = 24 + 3 + 3 = 30 units

∴ It takes Ramesh 8 days to complete the entire work if he is assisted by Suresh and Kamlesh every third day.

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