Time and Work
- If 5 men or 8 women can do a piece of work in 12 days, how many days will be taken by 2 men and 4 women to do the same work?
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According to the question
5 men = 8 women∴ 2 men = 8 × 2 = 16 women 5 5 ∴ Total women = 16 + 4 = 36 women 5 5
∴ No. of days to do the same work= 8 × 12 = 8 × 12 × 5 36/5 36 = 40 = 13 1 days 3 3
Aliter : Using Rule 12,
Here, A = 5, B = 8, a = 12
A1 = 2 and B1 = 4Time taken = a(A × B) A1B + B1A = 12(5 × 8) 2 × 8 + 4 × 5 = 12 × 40 36 = 33 1 days 3 Correct Option: C
According to the question
5 men = 8 women∴ 2 men = 8 × 2 = 16 women 5 5 ∴ Total women = 16 + 4 = 36 women 5 5
∴ No. of days to do the same work= 8 × 12 = 8 × 12 × 5 36/5 36 = 40 = 13 1 days 3 3
Aliter : Using Rule 12,
Here, A = 5, B = 8, a = 12
A1 = 2 and B1 = 4Time taken = a(A × B) A1B + B1A = 12(5 × 8) 2 × 8 + 4 × 5 = 12 × 40 36 = 33 1 days 3
- If 16 men or 20 women can do a piece of work in 25 days. In what time will 28 men and 15 women do it?
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16 men = 20 women 4 men = 5 women.
Now, according to question,
16 men complete the work in 25 days.
∴ 1 man one day’s work= 1 25 × 16
∴ 4 men one day’s work= 4 = 1 25 × 16 100
Similarly,
1 woman one day’s work= 1 25 × 20
∴ 5 women one day’s work= 5 = 1 25 × 20 100
∴ 28 men= 28 × 5 = 35 women 4
[28 men + 15 women]
∴ 50 women one day’s work= 50 = 1 25 × 20 10
Therefore, 28 men and 15 women can complete the whole work in 10 days.
Aliter : Using Rule 12,
A = 16, B = 20, a = 25
A1 = 28, B1 = 15Time taken = a(A × B) A1B1 + B1A = 25(16 × 20) 28 × 20 + 15 × 16 = 25 × 320 560 + 240 = 25 × 320 = 10 days 800 Correct Option: D
16 men = 20 women 4 men = 5 women.
Now, according to question,
16 men complete the work in 25 days.
∴ 1 man one day’s work= 1 25 × 16
∴ 4 men one day’s work= 4 = 1 25 × 16 100
Similarly,
1 woman one day’s work= 1 25 × 20
∴ 5 women one day’s work= 5 = 1 25 × 20 100
∴ 28 men= 28 × 5 = 35 women 4
[28 men + 15 women]
∴ 50 women one day’s work= 50 = 1 25 × 20 10
Therefore, 28 men and 15 women can complete the whole work in 10 days.
Aliter : Using Rule 12,
A = 16, B = 20, a = 25
A1 = 28, B1 = 15Time taken = a(A × B) A1B1 + B1A = 25(16 × 20) 28 × 20 + 15 × 16 = 25 × 320 560 + 240 = 25 × 320 = 10 days 800
- A man, a woman and a boy can complete a job in 3, 4 and 12 days respectively. How many boys must assist 1 man and 1 woman to complete the job in 1/4 of a day?
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1 man’s 1 day’s work = 1 3 1 woman’s 1 day’s work = 1 4 1 boy’s 1 day’s work = 1 12 (1 man + 1 woman)’s 1 day’s work 4 = 1 
1 + 1 
= 7 4 3 4 48
Remaining work= 1 – 7 = 41 48 48
Now,1 boy’s 1 day’s work 4 = 1 × 1 = 1 4 12 48 ∴ 41 work will be done by 41 × 48 = 41 boys. 48 48 Correct Option: D
1 man’s 1 day’s work = 1 3 1 woman’s 1 day’s work = 1 4 1 boy’s 1 day’s work = 1 12 (1 man + 1 woman)’s 1 day’s work 4 = 1 1 + 1 = 7 4 3 4 48
Remaining work= 1 – 7 = 41 48 48
Now,1 boy’s 1 day’s work 4 = 1 × 1 = 1 4 12 48 ∴ 41 work will be done by 41 × 48 = 41 boys. 48 48
- If 3 men or 6 women can do a piece of work in 16 days, in how many days can 12 men and 8 women do the same piece of work?
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3m = 6w
∴ 1m = 2w
12m + 8w = (12 × 2w) + 8w = 32w
∴ 6 women can do the work in 16 days.
∴ 32 women can do the work in16 × 6 = 3 days 32
Aliter : Using Rule 12,
Here, A = 3, B = 6, a = 16
A1 = 12, B1 = 8Time taken = a(A × B) A1B1 + B1A = 16(3 × 6) 12 × 6 + 8 × 3 = 16 × 18 = 3 days 96 Correct Option: C
3m = 6w
∴ 1m = 2w
12m + 8w = (12 × 2w) + 8w = 32w
∴ 6 women can do the work in 16 days.
∴ 32 women can do the work in16 × 6 = 3 days 32
Aliter : Using Rule 12,
Here, A = 3, B = 6, a = 16
A1 = 12, B1 = 8Time taken = a(A × B) A1B1 + B1A = 16(3 × 6) 12 × 6 + 8 × 3 = 16 × 18 = 3 days 96
- 5 men can do a piece of work in 6 days while 10 women can do it in 5 days. In how many days can 5 women and 3 men do it ?
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5 × 6 men = 10 × 5 women
⇒ 3 men = 5 women
∴ 5 women + 3 men = 6 men
∵ 5 men complete the work in 6 days
∴ 6 men will complete the work in= 5 × 6 = 5 days 6
Aliter : Using Rule 14,
Here, A = 5, a = 6
B = 10, b = 5
A1 = 3, B1 = 5Time taken = 1 A1 + B1 A × a B × b = 1 3 + 5 5 × 6 10 × 5 = 1 = 5 days 1 + 1 10 10 Correct Option: B
5 × 6 men = 10 × 5 women
⇒ 3 men = 5 women
∴ 5 women + 3 men = 6 men
∵ 5 men complete the work in 6 days
∴ 6 men will complete the work in= 5 × 6 = 5 days 6
Aliter : Using Rule 14,
Here, A = 5, a = 6
B = 10, b = 5
A1 = 3, B1 = 5Time taken = 1 A1 + B1 A × a B × b = 1 3 + 5 5 × 6 10 × 5 = 1 = 5 days 1 + 1 10 10
