Question

if 7 man or 8 woman or 10 boys can finish a piece of work in 24 days of 9 hours, find how many men with the help of 4 woman and 5 boys can finish it in 18 days of 6 hours

Answer 1

Find the amount of work 4 women can do in 1 hour:

8 women = 24 days of 9 hours = 216 hours

1 woman = 216 x 8 = 1728 hours

4 women = 1728 ÷ 4 = 432 hours

⇒ So 4 women can do 1/432 amount of work in 1 hour

Find the amount of work 5 boys can do in an hour:

10 boys = 24 days of 9 hours = 216 hours

1 boy = 216 x 10 = 2160 hours

5 boys = 2160 ÷ 5 = 432 hours

⇒ So 5 boys can do 1/432 amount of work in 1 hour

Find the amount of work 4 women and 5 boys can do in 18 days of 6 hours:

18 days of 6 hours = 108 hours

4 women, 1 hour = 1/432 amount of work

4 women, 108 hour = 1/432 x 108 = 1/4  amount of work

10 boys, 1 hour = 1/432 amount of work

10 boys, 108 hour = 1/432 x 108 = 1/4  amount of work

Total work = 1/4 + 1/4 = 1/2

⇒ 4 women and 5 boys can do 1/2 the work in 18 days of 6 hours

Find the remaining of the work:

Remaining work = 1 - 1/2 = 1/2

Find the number of days the men need:

7 men = 24 days of 9 hours = 24 x 9 = 216 hours

1 man = 216 x 7 = 1512 hours

⇒ 1 man can do 1/1512 of the work in 1 hour

1 hour = 1/1512 of the work

108 hours = 1/512 x 108 = 1/14 of the work

Number of men needed = 1/2 ÷ 1/14 = 7

Answer: 7 men are needed

Answer 2

Answer:

7 men

Step-by-step explanation:

• 7 men = 8 women = 10 boys completes the work in 24days of 9hours ie. 24×9= 216 hours

• 7 men = 8 women, therefore 7/2 men = 4 women
• 7 men = 10 boys, therefore 7/2 men = 5 boys---(1)

• To Find- X men + 4 women + 5 boys completes the work in 18 days of 6 hours ie. 108 hours.

By substituting (1) in the above equation,

X men + 7/2 men + 7/2 completes the work in 18 days of 6 hours ie. 108 hours.

• From the Formula M1 D1 = M2 D2

7 men × 216 hours = ( x + 7/2 + 7/2) × 108

7 × 216 = ( 2x + 7 + 7)

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108 2

7 × 216 × 2 = 2x + 14

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108

28 = 2x + 14

x = 14 / 2 = 7 men.