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A company entrusts work to 16 men working 10 hours a day. This group can complete the work in 20 days. The company now entrust twice the work to 50 men working 4 hours a day. Assume that 2 men of the first group do as much work in 1 hour as 3 men of second group in \(1\frac{1}{2}\) hours. How many number of days will the second group take to complete the work?

A company entrusts work to 16 men working 10 hours a day. This group can complete the work in 20 days. The company now entrust twice the work to 50 men working 4 hours a day. Assume that 2 men of the first group do as much work in 1 hour as 3 men of second group in \(1\frac{1}{2}\) hours. How many number of days will the second group take to complete the work? Correct Answer 72

Let efficiency of men in first group be X and that of second group be Y

Ratios of efficiency X/Y = time taken by men in second group/ time taken by men in first group to complete the same task

⇒ X/Y = (3 × 1.5) : (2 × 1)

⇒ X/Y = 4.5 : 2

We know that,

Man × days × time × efficiency is directly proportional to work

⇒ 16 × 20 × 10 × X = k × work

Similarly,

⇒ 50 × days × 4 × Y = k × twice the work

Dividing both,

⇒ (16 × 20 × 10 × X)/(50 × days × 4 × Y) = work/twice the work

⇒ 16X/(days × Y) = 1/2

⇒ 16/days × 4.5/2 = 1/2

⇒ 36/days = 1/2

∴ Days = 36 × 2 = 72 days

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