Question

1200 men and 500 women can build a bridge in 2 weeks. 900 men and 250 women will take 3 weeks to build same bridge . how many men will needed to build same bridge in one week

Answer 1

it may be 1500 men and 750 women

Answer 2

3600 men will be needed to build the same bridge in 1 week.

Step-by-step explanation:

It is given that,

1200M + 500W can build a bridge in 2 weeks i.e., 2*7 = 14 days

And

900M + 250W can build a bridge in 3 weeks i.e., 3*7 = 21 days

Since the work done in both the cases are same i.e., both will build a bridge, therefore, by using the Man-Days formula we can compare both the cases as,

(1200M + 500W) * 14 = (900M + 250W) * 21

⇒ (1200M + 500W) * 2 = (900M + 250W) * 3

⇒ 2400M + 1000W = 2700M + 750W

⇒ 250W = 300M

⇒ W = (6/5) * M ...... (i)

Now, substituting from (i), we have

900M + 250W = 900M + 250*(6/5)M = 900M + 300M = 1200M ← can build the bridge in 3 weeks i.e., 21 days.

Therefore, again by using the Man-days formula, we get

1200M * 21 days = [required no. of men] * 7 days

⇒ Required no. of men = 3600

Thus, a total of 3600 men are required to build the same bridge in 1 week.

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