Time and Work
- A sum of money is sufficient to pay A’ s wages for 21 days and B’s wages for 28 days. The same money is sufficient to pay the wages of both for :
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A's 1 day's work = 1 21 B's 1 day's work = 1 28
Total work done by both= 1 + 1 = 4 + 3 = 1 21 28 84 12
∴ Amount is sufficient to pay 12 days wages of both.
Aliter : Using Rule 2,
Here, x = 21, y = 28
Required days= x × y = 21 × 28 x + y 21 + 28 = 21 × 28 = 12 days 49 Correct Option: D
A's 1 day's work = 1 21 B's 1 day's work = 1 28
Total work done by both= 1 + 1 = 4 + 3 = 1 21 28 84 12
∴ Amount is sufficient to pay 12 days wages of both.
Aliter : Using Rule 2,
Here, x = 21, y = 28
Required days= x × y = 21 × 28 x + y 21 + 28 = 21 × 28 = 12 days 49
- A can do a piece of work in 12 days while B alone can do it in 15 days. With the help of C they can finish it in 5 days. If they are paid ₹ 960 for the whole work how much money A gets ?
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Rule 2 and Rule 25,
Work done by A and B in 5 days= 5 
1 + 1 
= 5 5 + 4 12 15 60 = 9 = 3 12 4 Time taken by C in doing 1 work = 5 days 4
∴ C will complete in 20 days.∴ Ratio of wages = 1 : 1 : 5 = 5 : 4 : 3 12 15 20
∴ Amount received by A= 5 × 960 = ₹ 400 12 Correct Option: D
Rule 2 and Rule 25,
Work done by A and B in 5 days= 5 1 + 1 = 5 5 + 4 12 15 60 = 9 = 3 12 4 Time taken by C in doing 1 work = 5 days 4
∴ C will complete in 20 days.∴ Ratio of wages = 1 : 1 : 5 = 5 : 4 : 3 12 15 20
∴ Amount received by A= 5 × 960 = ₹ 400 12
- A, B and C together earn ₹ 150 per day while A and C together earn ₹ 94 and B and C together earn ₹ 76. The daily earning of ‘C’ is
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The daily earning of ‘C’ = Daily earning of (A + C) and
(B + C) – Daily earning of
(A + B + C) = 94 + 76 – 150
= ₹ 20Correct Option: B
The daily earning of ‘C’ = Daily earning of (A + C) and
(B + C) – Daily earning of
(A + B + C) = 94 + 76 – 150
= ₹ 20
- Three persons undertake to complete a piece of work for ₹ 1,200. The first person can complete the work in 8 days, second person in 12 days and third person in 16 days. They complete the work with the help of a fourth person in 3 days. What does the fourth person get?
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Rule 3 and Rule 25,
If the fourth person completes the work in x days, then3 + 3 + 3 + 3 = 1 8 12 16 x ⇒ 1 = 1 - 1 - 1 - 1 x 3 8 12 16 = 16 - 6 - 4 - 3 = 1 48 16
∴ x = 16
∴ Ratio of wages= 1 : 1 : 1 : 1 = 6 : 4 : 3 : 3 8 12 16 16
Sum of ratios = 6 + 4 + 3 + 3 = 16
∴ Fourth person’s share= 3 × 1200 = ₹ 225 12 Correct Option: C
Rule 3 and Rule 25,
If the fourth person completes the work in x days, then3 + 3 + 3 + 3 = 1 8 12 16 x ⇒ 1 = 1 - 1 - 1 - 1 x 3 8 12 16 = 16 - 6 - 4 - 3 = 1 48 16
∴ x = 16
∴ Ratio of wages= 1 : 1 : 1 : 1 = 6 : 4 : 3 : 3 8 12 16 16
Sum of ratios = 6 + 4 + 3 + 3 = 16
∴ Fourth person’s share= 3 × 1200 = ₹ 225 12
- A and B working separately can do a piece of work in 9 and 15 days respectively. If they work for a day alternately, with A beginning, then the work will be completed in
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A’s 1 day’s work = 1 9 B’s 1 day’s work = 1 15
Work done in first 2 days = A’s 1 day’s work + B’s 1 day’s workWork done in first 2 days = 1 + 1 9 15 Work done in first 2 days = 5 + 3 = 8 45 45 ∴ Work done in first 10 days = 8 × 5 = 8 45 9 Remaining work = 1 – 8 = 1 9 9
Now, it is turn of ‘A’ for the eleventh day.
Correct Option: B
A’s 1 day’s work = 1 9 B’s 1 day’s work = 1 15
Work done in first 2 days = A’s 1 day’s work + B’s 1 day’s workWork done in first 2 days = 1 + 1 9 15 Work done in first 2 days = 5 + 3 = 8 45 45 ∴ Work done in first 10 days = 8 × 5 = 8 45 9 Remaining work = 1 – 8 = 1 9 9
Now, it is turn of ‘A’ for the eleventh day.∴ Time taken by ‘A’ in doing 1 work 9 = 1 × 9 = 1 day 9
∴ Required time = 10 + 1 = 11 days
