Time and Work
- If 4 men or 6 women can do a piece of work in 12 days working 7 hours a day; how many days will it take to complete a work twice as large with 10 men and 3 women working together 8 hours a day?
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View Hint View Answer Discuss in Forum
Using Rule 1,
4 men ≡ 6 women1 men ≡ 6 = 3 woman 4 2
= women 10 men + 3 women= 10 × 3 + 3 = 18 woman 2 ∴ M1D1T1 = M2D2T2 W1 W2 ⇒ 6 × 12 × 7 = 8 × D2 × 8 1 W2 ⇒ D2 = 6 × 12 × 7 × 2 = 7 days 18 × 8 Correct Option: B
Using Rule 1,
4 men ≡ 6 women1 men ≡ 6 = 3 woman 4 2
= women 10 men + 3 women= 10 × 3 + 3 = 18 woman 2 ∴ M1D1T1 = M2D2T2 W1 W2 ⇒ 6 × 12 × 7 = 8 × D2 × 8 1 W2 ⇒ D2 = 6 × 12 × 7 × 2 = 7 days 18 × 8
- 3 men or 5 women can do a work in 12 days. How long will 6 men and 5 women take to finish the work?
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View Hint View Answer Discuss in Forum
3 men’s work = 5 women’s work
1 man’s work = 5 women’s work 3 ∴ 6 men’s work = 5 × 6 3
=10 women’s work
∴ 6 men + 5 women = 15 women
∴ 5 women can do work in 12 days.
Hence, 15 women can do it in5 × 12 = 4 days 15
Aliter : Using Rule 12,
Here, A = 3, B = 5, a = 12
A1 = 6 and B1 = 5Required time = a(A × B) A1B + B1A
= 12(3 × 5) 6 × 5 + 5 × 3 = 12 × 15 = 4 days 45 Correct Option: C
3 men’s work = 5 women’s work
1 man’s work = 5 women’s work 3 ∴ 6 men’s work = 5 × 6 3
=10 women’s work
∴ 6 men + 5 women = 15 women
∴ 5 women can do work in 12 days.
Hence, 15 women can do it in5 × 12 = 4 days 15
Aliter : Using Rule 12,
Here, A = 3, B = 5, a = 12
A1 = 6 and B1 = 5Required time = a(A × B) A1B + B1A
= 12(3 × 5) 6 × 5 + 5 × 3 = 12 × 15 = 4 days 45
- A man, a woman and a boy can together complete a piece of work in 3 days. If a man alone can do it in 6 days and a boy alone in 18 days, how long will a woman alone take to complete the work?
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View Hint View Answer Discuss in Forum
Work done by 1 woman in 1 day
= 1 - 1 - 1 3 6 18 = 6 - 3 - 1 = 1 18 9
∴ Woman will do the work in 9 days.
Aliter : Using Rule 18,
Here, x = 3, y = 6 and z = 18
∴ Required time= xyz days yz - x(y + z) = 3 × 6 × 18 6 × 18 - 3(6 + 18) = 324 108 - 3 × 24 = 324 = 9 36 Correct Option: A
Work done by 1 woman in 1 day
= 1 - 1 - 1 3 6 18 = 6 - 3 - 1 = 1 18 9
∴ Woman will do the work in 9 days.
Aliter : Using Rule 18,
Here, x = 3, y = 6 and z = 18
∴ Required time= xyz days yz - x(y + z) = 3 × 6 × 18 6 × 18 - 3(6 + 18) = 324 108 - 3 × 24 = 324 = 9 36
- 6 men or 12 women can do a piece of work in 20 days. In how many days can 8 men and 16 women do twice as big as this work ?
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View Hint View Answer Discuss in Forum
6 men = 12 women
∴ 1 man = 2 women
Now, 8 men + 16 women
= (8 × 2 + 16) women = 32 women
∵ 12 women can do a work in 20 days.
∴ 1 woman can do the work in 20 × 12 days.
∴ 32 women can do the twice work in= 20 × 12 × 2 = 15 days 32
Aliter : Using Rule 12,
Here, A = 6, B= 12, a = 20
A1 = 8, B1 = 16Time taken = a(A × B) A1B + B1A = 20 (6 × 12) 8 × 12 + 16 × 6 = 20 × 72 = 15 192 2
They will do the twice as big work in2 × 15 days = 15 days 2 Correct Option: C
6 men = 12 women
∴ 1 man = 2 women
Now, 8 men + 16 women
= (8 × 2 + 16) women = 32 women
∵ 12 women can do a work in 20 days.
∴ 1 woman can do the work in 20 × 12 days.
∴ 32 women can do the twice work in= 20 × 12 × 2 = 15 days 32
Aliter : Using Rule 12,
Here, A = 6, B= 12, a = 20
A1 = 8, B1 = 16Time taken = a(A × B) A1B + B1A = 20 (6 × 12) 8 × 12 + 16 × 6 = 20 × 72 = 15 192 2
They will do the twice as big work in2 × 15 days = 15 days 2
- If 3 men or 4 women can plough a field in 43 days, how long will 7 men and 5 women take to plough it ?
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View Hint View Answer Discuss in Forum
∵ 3 men = 4 women
∴ 1 man = 4 women 3 ∴ 7 men = 7 × 4 = 28 women 3 3 ∴ 7 men + 5 women = 28 + 5 3 = 28 + 15 = 43 women 3 3
Now, M1D1 = M2 D2⇒ 4 × 43 = 43 × D2 3
Aliter : Using Rule 12,
Here, A = 3, B = 4, a = 43
A1 = 7 and B1 = 5Time taken = a(A × B) A1B + B1A = 43 × 12 = 12 days 43 Correct Option: D
∵ 3 men = 4 women
∴ 1 man = 4 women 3 ∴ 7 men = 7 × 4 = 28 women 3 3 ∴ 7 men + 5 women = 28 + 5 3 = 28 + 15 = 43 women 3 3
Now, M1D1 = M2 D2⇒ 4 × 43 = 43 × D2 3
Aliter : Using Rule 12,
Here, A = 3, B = 4, a = 43
A1 = 7 and B1 = 5Time taken = a(A × B) A1B + B1A = 43 × 12 = 12 days 43
