Time and Work
- 24 boys can complete a work in 12 days while 16 men can complete the same work in 9 days. In How many days will 12 boys and 12 men together complete the same work ?
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∵ In 12 days the work is done by = 24 boys
∴ In 1 day the work is done by = 24 x 12 = 288 boys
∵ In 9 days the work is done by = 16 men
∴ 1 day work is done by = 16 x 9 = 144 men
⇒ 144 men = 288 boys
⇒ 1 men = 288/144 = 2 boysCorrect Option: B
∵ In 12 days the work is done by = 24 boys
∴ In 1 day the work is done by = 24 x 12 = 288 boys
∵ In 9 days the work is done by = 16 men
∴ 1 day work is done by = 16 x 9 = 144 men
⇒ 144 men = 288 boys
⇒ 1 men = 288/144 = 2 boys
⇒ 12 men + 12 boys = 12 x 2 + 12 = 36 boys
∵ 24 boys complete 1 work in 12 days
∴ 36 boys complete 1 work in (12 x 24)/36 = 8 days
- 14 workers can make 1400 toys in 5 days. One day after they started the work 14 more workers joined them. How many days will they take to complete the remaining work ?
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∵ In 5 days 14 workers make = 1400 toys.
∴ In 1 days 14 workers make toys = 1400/5 = 280 toys.
Number of remaining toys = 1400 - 280 = 1120
and number of total workers = 14 + 14 = 28
∵ 14 workers make 1400 toys in 5 days.Correct Option: A
∵ In 5 days 14 workers make = 1400 toys.
∴ In 1 days 14 workers make toys = 1400/5 = 280 toys.
Number of remaining toys = 1400 - 280 = 1120
and number of total workers = 14 + 14 = 28
∵ 14 workers make 1400 toys in 5 days.
∴ 28 workers make 1120 toys = (5 x 14 x 1120)/(28 x 1400) = 2 days
- 14 men can complete a work in 12 days. 4 days after they started the work, 2 more men joined them. How many days will they take to complete the remaining work ?
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∵ In 12 days work done by 14 men = 1
∴ In 4 days work done by 14 men = 1 x 4/12 = 1/3
∴ Remaining work = 1 - 1/3 = 2/3
and number of total men = 14 + 2 = 16Correct Option: D
∵ In 12 days work done by 14 men = 1
∴ In 4 days work done by 14 men = 1 x 4/12 = 1/3
∴ Remaining work = 1 - 1/3 = 2/3
and number of total men = 14 + 2 = 16
If 1 work is done by 14 men in 12 days
∴ 2/3 work is done by 16 men in 12 x (14/16) x (2/3) = 7 days
- A and B can do a piece of work in 8 days, B and C can do the same work in 12 days and A and C complete it in 8 days. In how many days A, B and C can complete the whole work,working together?
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Efficiency of (A + B) = 12.5%
Efficiency of (B + C) = 8.33%
Efficiency of (C + A) = 12.5%
∴ Efficiency of [(A + B) + (B + C) + (C + A)] = 33.33%Correct Option: B
Efficiency of (A + B) = 12.5%
Efficiency of (B + C) = 8.33%
Efficiency of (C + A) = 12.5%
∴ Efficiency of [(A + B) + (B + C) + (C + A)] = 33.33%
∴ Efficiency of (A + B + C) = 16.66%
∴ No. of days Required by A, B and C together = 100/16.66 = 6 days
- A and B can do a piece of work in 12 days B and C in 15 days C and A in 20 days. In how many days can C alone do it?
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Efficiency of (A + B) = 8.33%
Efficiency of (B + C) = 6.66%
Efficiency of (C + A) = 5.00%
∴ Efficiency of A + B + C = (8.33 + 6.66 + 5) / 2 = 10%
∴ Efficiency of C = Efficiency of [(A + B + C) - (A + B) ]
= (10 - 8.33) = 1.66%Correct Option: A
Efficiency of (A + B) = 8.33%
Efficiency of (B + C) = 6.66%
Efficiency of (C + A) = 5.00%
∴ Efficiency of A + B + C = (8.33 + 6.66 + 5) / 2 = 10%
∴ Efficiency of C = Efficiency of [(A + B + C) - (A + B) ]
= (10 - 8.33) = 1.66%
∴ No. of days required by C alone = 100/1.66 = 60days
