Time and Work
- A certain number of men can complete a job in 30 days. If there were 5 men more, it could be completed in 10 days less. How many men were in the beginning?
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Let initially the number of men be x.
⇒ According to question,
M1D1 W2 = M2 D2 W1
x × 30 = (x + 5) × (30 – 10)
x × 30 = 20x + 100
30x – 20x = 100
10x = 100
x = 10
Aliter : Using Rule 23,
Here, D = 30, a = 5, d = 10
Required number= a(D - d) d = 5(30 - 10) = 10 10 Correct Option: A
Let initially the number of men be x.
⇒ According to question,
M1D1 W2 = M2 D2 W1
x × 30 = (x + 5) × (30 – 10)
x × 30 = 20x + 100
30x – 20x = 100
10x = 100
x = 10
Aliter : Using Rule 23,
Here, D = 30, a = 5, d = 10
Required number= a(D - d) d = 5(30 - 10) = 10 10
- A skilled, a half skilled and an unskilled labourer work for 7, 8 and 10 days respectively and they together get 369 for their work. If the ratio of their each day’s work is
1 : 1 : 1 3 4 6
then how much does the trained labourer get (in rupees) ?
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Using Rule 25,
Skilled : half skilled : unskilled= 1 : 1 : 1 3 4 6 = 
1 × 12 
: 1 × 12 : 1 × 12 = 4 : 3 : 2 3 4 6
Share of the trained labourer= 28 × 369 (7 × 4 + 8 × 3 + 2 × 10) = 28 × 369 (28 + 24 + 20) = 28 × 369 = ₹ 143.50 72 Correct Option: D
Using Rule 25,
Skilled : half skilled : unskilled= 1 : 1 : 1 3 4 6 = 1 × 12 : 1 × 12 : 1 × 12 = 4 : 3 : 2 3 4 6
Share of the trained labourer= 28 × 369 (7 × 4 + 8 × 3 + 2 × 10) = 28 × 369 (28 + 24 + 20) = 28 × 369 = ₹ 143.50 72
- A, B and C are employed to do a piece of work for ₹ 575. A and C are supposed to finish 19/23 of the work together. Amount shall be paid to B is
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Work done by B
= 1 - 19 = 23 - 19 = 4 23 23 23 ∴ (A + C) : B = 19 : 4 = 19 : 4 23 23
∴ Sum of ratios = 19 + 4 = 23
∴ B’s share= 4 × 575 = ₹ 100 23 Correct Option: B
Work done by B
= 1 - 19 = 23 - 19 = 4 23 23 23 ∴ (A + C) : B = 19 : 4 = 19 : 4 23 23
∴ Sum of ratios = 19 + 4 = 23
∴ B’s share= 4 × 575 = ₹ 100 23
- If a man earns ₹ 2000 for his first 50 hours of work in a week and is then paid one and a half times his regular hourly rate for any additional hours, then the hours must he work to make ₹ 2300 in a week is
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Earning in the first one hour
= 2000 = Rs. 40 50
Earnings for additional 5 hours= 40 × 3 × 5 = Rs. 300 2 Correct Option: D
Earning in the first one hour
= 2000 = Rs. 40 50
Earnings for additional 5 hours= 40 × 3 × 5 = Rs. 300 2
- 2 men and 1 woman can complete a piece of work in 14 days while 4 women and 2 men can do the same work in 8 days. If a man gets Rs. 180 per day, then a woman will get per day
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(2 men + 1 woman)’s 14 days’ work ≡ (4 women + 2 men)’s 8 days’ work
⇒ 28 men + 14 women ≡ 32 women + 16 men
⇒ (28 – 16) = 12 men ≡ (32 – 14) = 18 women
⇒ 2 men ≡ 3 women∴ 1 woman ≡ 2 man 3
∵ Wages per day of 1 man = Rs. 180
∴ Wages per day of 1 woman= 2 × 180 = Rs. 120 3 Correct Option: C
(2 men + 1 woman)’s 14 days’ work ≡ (4 women + 2 men)’s 8 days’ work
⇒ 28 men + 14 women ≡ 32 women + 16 men
⇒ (28 – 16) = 12 men ≡ (32 – 14) = 18 women
⇒ 2 men ≡ 3 women∴ 1 woman ≡ 2 man 3
∵ Wages per day of 1 man = Rs. 180
∴ Wages per day of 1 woman= 2 × 180 = Rs. 120 3
