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
Answers
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:
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.