Time and Work
- A can do 1/6 of a work in 5 days and B can do 2/5 of the work in 8 days. In how many days, can both A and B together do the work?
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Using basics of Rule 2,
Time taken by A to finish the work = 5 × 6 = 30 days
Time taken by B to complete the work= 8 × 5 = 20 days 2
∴ (A + B)'s 1 day’s work= 1 + 1 = 2 + 3 = 1 30 20 60 12
∴ Required time = 12 daysCorrect Option: A
Using basics of Rule 2,
Time taken by A to finish the work = 5 × 6 = 30 days
Time taken by B to complete the work= 8 × 5 = 20 days 2
∴ (A + B)'s 1 day’s work= 1 + 1 = 2 + 3 = 1 30 20 60 12
∴ Required time = 12 days
- 3 men and 5 women can do a work in 14 days while 5 men can do it in 14 days. 5 men and 5 women can complete the work in
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∵ 5 men can do 1 work in 14 days.
∴ 3 men will do 3 work in 14 days. 5 Remaining work = 1 - 3 = 2 5 5 ∴ 5 women do 2 work in 14 days. 5 ∴ Time taken by 5 women in doing 1 work 14 × 5 = 35 days. 2
∴ (5 men + 5 women)’s 1 day’s work= 1 + 1 = 5 + 2 = 7 = 1 14 35 70 70 10
∴ Required time = 10 days.Correct Option: C
∵ 5 men can do 1 work in 14 days.
∴ 3 men will do 3 work in 14 days. 5 Remaining work = 1 - 3 = 2 5 5 ∴ 5 women do 2 work in 14 days. 5 ∴ Time taken by 5 women in doing 1 work 14 × 5 = 35 days. 2
∴ (5 men + 5 women)’s 1 day’s work= 1 + 1 = 5 + 2 = 7 = 1 14 35 70 70 10
∴ Required time = 10 days.
- 18 men or 36 boys working 6 hours a day can plough a field in 24 days. In how many days will 24 men and 24 boys working 9 hours a day plough the same field ?
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18 men ≡ 36 boys
⇒ 1 man ≡ 2 boys
∴ 24 men + 24 boys
≡ (24 + 12) men
≡ 36 men
M1D1T1 = M2D2T2
⇒ 18 × 24 × 6 = 36 × D2 × 9⇒ D2 = 18 × 24 × 6 = 8 days 36 × 9 Correct Option: D
18 men ≡ 36 boys
⇒ 1 man ≡ 2 boys
∴ 24 men + 24 boys
≡ (24 + 12) men
≡ 36 men
M1D1T1 = M2D2T2
⇒ 18 × 24 × 6 = 36 × D2 × 9⇒ D2 = 18 × 24 × 6 = 8 days 36 × 9
- Twenty women can do a work in sixteen days. Sixteen men can complete the same work in fifteen days. The ratio between the capacity of a man and a woman is
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20 women complete 1 work in 16 days.
16 men complete same work in 15 days
∴ 16 × 15 men ≡ 20 × 16 women
⇒ 3 men ≡ 4 women
∴ Required ratio = 4 : 3Correct Option: B
20 women complete 1 work in 16 days.
16 men complete same work in 15 days
∴ 16 × 15 men ≡ 20 × 16 women
⇒ 3 men ≡ 4 women
∴ Required ratio = 4 : 3
- 12 men and 16 boys can do a piece of work in 5 days; 13 men and 24 boys can do it in 4 days, then the ratio of the daily work done by a man to that of a boy is
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Work done by 12 men + 16 boys in 5 days
≡ Work done 13 men + 24 boys in 4 days
→ (60 men + 80 boys)’s 1 day’s work ≡ (52 men + 96 boys)’s 1 day’s work
⇒ (60 – 52) men ≡ (96 – 80) boys
⇒ 8 men ≡ 16 boys
⇒ 1 man ≡ 2 boys
∴ Required ratio = 2 : 1Correct Option: A
Work done by 12 men + 16 boys in 5 days
≡ Work done 13 men + 24 boys in 4 days
→ (60 men + 80 boys)’s 1 day’s work ≡ (52 men + 96 boys)’s 1 day’s work
⇒ (60 – 52) men ≡ (96 – 80) boys
⇒ 8 men ≡ 16 boys
⇒ 1 man ≡ 2 boys
∴ Required ratio = 2 : 1
