Time and Work
- A daily-wage labourer was engaged for a certain number of days for ₹ 5,750; but being absent on some of those days he was paid only ₹ 5,000. What was his maximum possible daily wage?
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It is required to find the highest common factor of 5750 and 5000, because his daily wage is their common factor.
Hence, the daily wage is ₹ 250Correct Option: B
It is required to find the highest common factor of 5750 and 5000, because his daily wage is their common factor.
Hence, the daily wage is ₹ 250
- A, B and C completed a work costing ₹ 1,800. A worked for 6 days, B for 4 days and C for 9 days. If their daily wages are in the ratio of 5 : 6 : 4, how much amount will be received by A?
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Using Rule 25,
Ratio of wages of A, B and C respectively
= 5 × 6 : 6 × 4 : 4 × 9
= 30 : 24 : 36 = 5 : 4 : 6
∴ Amount received by A= 5 × 1800 5 + 4 + 6 = 5 × 1800 = ₹ 600 15 Correct Option: B
Using Rule 25,
Ratio of wages of A, B and C respectively
= 5 × 6 : 6 × 4 : 4 × 9
= 30 : 24 : 36 = 5 : 4 : 6
∴ Amount received by A= 5 × 1800 5 + 4 + 6 = 5 × 1800 = ₹ 600 15
- A labourer was appointed by a contractor on the condition that he would be paid ₹ 75 for each day of his work but would be fined at the rate of ₹ 15 per day for his absence, apart from losing his wages, After 20 days, the contractor paid the labourer ₹ 1140. The number of days the labourer abstained from work was
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Total salary for 20 days
= ₹ (75 × 20) = ₹ 1500
Actual salary received = ₹ 1140
Difference = ₹ (1500 – 1140) = ₹ 360
Money deducted for 1 day’s absence from work
= ₹ (15 + 75) = ₹ 90
∴ Number of days he wasabsent = 360 = 4 days 90 Correct Option: C
Total salary for 20 days
= ₹ (75 × 20) = ₹ 1500
Actual salary received = ₹ 1140
Difference = ₹ (1500 – 1140) = ₹ 360
Money deducted for 1 day’s absence from work
= ₹ (15 + 75) = ₹ 90
∴ Number of days he wasabsent = 360 = 4 days 90
- Two men undertook to do a job for ₹ 1400. One of them can do it alone in 7 days, and the other in 8 days. With the assistance of a boy they together completed the work in 3 days. How much money will the boy get ?
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Using Rule 25,
First man’s 1 day’s work = 1 7 Second man’s 1 day’s work = 1 8 Let, Boy’s 1 day’s work = 1 x ∴ 1 + 1 + 1 = 1 7 8 x 3 ⇒ 1 = 1 - 1 - 1 x 3 7 8 = 56 - 24 - 21 = 11 168 168
∴ Ratio of their one day’s work1 : 1 : 1 = 24 : 21 : 11 7 8 168
Sum of the ratios
= 24 + 21 + 11= 56
∴ Boy’s share in wages= 11 × 1400 = ₹ 275 56 Correct Option: C
Using Rule 25,
First man’s 1 day’s work = 1 7 Second man’s 1 day’s work = 1 8 Let, Boy’s 1 day’s work = 1 x ∴ 1 + 1 + 1 = 1 7 8 x 3 ⇒ 1 = 1 - 1 - 1 x 3 7 8 = 56 - 24 - 21 = 11 168 168
∴ Ratio of their one day’s work1 : 1 : 1 = 24 : 21 : 11 7 8 168
Sum of the ratios
= 24 + 21 + 11= 56
∴ Boy’s share in wages= 11 × 1400 = ₹ 275 56
- If 5 men or 7 women can earn ₹ 5,250 per day, how much would 7 men and 13 women earn per day ?
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5 men ≡ 7 women
[Both earn same amount in 1 day]∴ 7 men ≡ 7 × 7 = 49 women 5 5
∴ 7 men + 13 women= 49 + 13 = 114 women 5 5
Now,
∵ 7 women ≡ ₹ 5250∴ 114 women 5 = 5250 × 114 = ₹ 17100 5 5 Correct Option: D
5 men ≡ 7 women
[Both earn same amount in 1 day]∴ 7 men ≡ 7 × 7 = 49 women 5 5
∴ 7 men + 13 women= 49 + 13 = 114 women 5 5
Now,
∵ 7 women ≡ ₹ 5250∴ 114 women 5 = 5250 × 114 = ₹ 17100 5 5
