Time and Work
- A certain number of men complete a piece of work in 60 days. If there were 8 men more, the work could be finished in 10 days less. The number of men originally was
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Number of men originally = x (let)
∴ M1 D1 = M2 D2
⇒ x × 60 = (x + 8) × 50
⇒ 6x = 5x + 40
⇒ 6x – 5x = 40
⇒ x = 40 men
Aliter : Using Rule 23,
Here, D= 60, a = 8, d =10∴ Required number= a(D - d) d = 8(60 - 10) = 40 10 Correct Option: B
Number of men originally = x (let)
∴ M1 D1 = M2 D2
⇒ x × 60 = (x + 8) × 50
⇒ 6x = 5x + 40
⇒ 6x – 5x = 40
⇒ x = 40 men
Aliter : Using Rule 23,
Here, D= 60, a = 8, d =10∴ Required number= a(D - d) d = 8(60 - 10) = 40 10
- A, B and C together can do a piece of work in 40 days. After working with B and C for 16 days, A leaves and then B and C complete the remaining work in 40 days more. A alone could do the work in
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A, B and C together complete the work in 40 days.
∴ (A + B + C)’s 1 day’s work= 1 40
∴ (A + B + C)’s 16 days work= 16 = 2 40 5 Remaining work = 1 – 2 = 3 5 5
This part of work is done by B and C in 40 days.∴ Time taken in doing 3 work = 40 days. 5
∴ Time taken in doing in 1 work= 40 × 5 = 200 days 3 3
∴ A’s day’s work = (A + B + C)’s 1 day’s work – (B + C)’s 1 day’s work= 1 - 3 40 200 = 5 - 3 = 2 = 1 200 200 100
∴ Required time = 100 daysCorrect Option: C
A, B and C together complete the work in 40 days.
∴ (A + B + C)’s 1 day’s work= 1 40
∴ (A + B + C)’s 16 days work= 16 = 2 40 5 Remaining work = 1 – 2 = 3 5 5
This part of work is done by B and C in 40 days.∴ Time taken in doing 3 work = 40 days. 5
∴ Time taken in doing in 1 work= 40 × 5 = 200 days 3 3
∴ A’s day’s work = (A + B + C)’s 1 day’s work – (B + C)’s 1 day’s work= 1 - 3 40 200 = 5 - 3 = 2 = 1 200 200 100
∴ Required time = 100 days
- If 12 men or 24 boys can do a work in 66 days, the number of days in which 15 men and 6 boys can do it is
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&because12 men ≡24 boys
∴ 1 man ≡2 boys
∴ 15 men + 6 boys
= 30 boys + 6 boys = 36 boys
∴ M1D1 = M2D2
⇒ 24 × 66 = 36 × D2⇒ D2 = 24 × 66 = 44 days 36
Aliter : Using Rule 12,
Here, A = 12, B = 24
a = 66, A1 = 15, B1 = 6∴ Time taken = a ( A × B) A1B + B1A = 66 ( 12 × 24) 15 × 24 + 6 × 12 = 66 × 288 360 + 72 = 66 × 288 = 44 days. 432 Correct Option: A
&because12 men ≡24 boys
∴ 1 man ≡2 boys
∴ 15 men + 6 boys
= 30 boys + 6 boys = 36 boys
∴ M1D1 = M2D2
⇒ 24 × 66 = 36 × D2⇒ D2 = 24 × 66 = 44 days 36
Aliter : Using Rule 12,
Here, A = 12, B = 24
a = 66, A1 = 15, B1 = 6∴ Time taken = a ( A × B) A1B + B1A = 66 ( 12 × 24) 15 × 24 + 6 × 12 = 66 × 288 360 + 72 = 66 × 288 = 44 days. 432
- 40 men can complete a work in 18 days. Eight days after they started working together, 10 more men joined them. How many days will they now take to complete the remaining work ?
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40 men complete the work in 18 days.
∴ Their 1 day’s work = 1 18 ∴ Their 8 days’ work = 8 = 4 18 9 Remaining work = 1 – 4 = 5 9 9
New number of men = 40 + 10 = 50∴ M1D1 = M2D2 W1 W2 ⇒ 40 × 18 = 50 × D2 1 5/9
⇒ 40 × 18 = 90 × D2⇒ D2 = 40 × 18 = 8 days. 90
Aliter : Using Rule 10,
Here, A = 40, a = 18
b = 8, B = 10Required Days = A(a - b) (A + B) = 40(18 - 8) (40 + 10) = 40 × 10 = 8 days 50 Correct Option: B
40 men complete the work in 18 days.
∴ Their 1 day’s work = 1 18 ∴ Their 8 days’ work = 8 = 4 18 9 Remaining work = 1 – 4 = 5 9 9
New number of men = 40 + 10 = 50∴ M1D1 = M2D2 W1 W2 ⇒ 40 × 18 = 50 × D2 1 5/9
⇒ 40 × 18 = 90 × D2⇒ D2 = 40 × 18 = 8 days. 90
Aliter : Using Rule 10,
Here, A = 40, a = 18
b = 8, B = 10Required Days = A(a - b) (A + B) = 40(18 - 8) (40 + 10) = 40 × 10 = 8 days 50
- 16 women take 12 days to complete a work which can be completed by 12 men in 8 days. 16 men started working and after 3 days 10 men left and 4 women joined them. How many days will it take them to complete the remaining work ?
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Work done by 12 men in 8 days ≡ Work done by 16 women in 12 days.
⇒ 12 × 8 men ≡ 16 × 12 women
⇒ 1 man ≡ 2 women
Now, work done by 12 men in 1 day= 1 8
1 man’s 1 day’s work= 1 = 1 12 × 8 96
∴ 16 men’s 3 day’s workRemaining work = 1 – 1 = 1 2 2 Now 1 work is done by 6 men and 4 women. 2
∴ 6 men + 4 women
= (6 + 2) men = 8 men∴ M1D1 = M2D2 W1 W2 ∴ 12 × 8 = 8 × D2 1 1/2 ⇒ D2 = 12 × 8 = 6 days. 2 × 8 Correct Option: B
Work done by 12 men in 8 days ≡ Work done by 16 women in 12 days.
⇒ 12 × 8 men ≡ 16 × 12 women
⇒ 1 man ≡ 2 women
Now, work done by 12 men in 1 day= 1 8
1 man’s 1 day’s work= 1 = 1 12 × 8 96
∴ 16 men’s 3 day’s workRemaining work = 1 – 1 = 1 2 2 Now 1 work is done by 6 men and 4 women. 2
∴ 6 men + 4 women
= (6 + 2) men = 8 men∴ M1D1 = M2D2 W1 W2 ∴ 12 × 8 = 8 × D2 1 1/2 ⇒ D2 = 12 × 8 = 6 days. 2 × 8
