Time and Work
- A certain number of men can do a piece of work in 60 days. If there were 6 men more, the work can be finished 20 days earlier. The number of men working is :
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Let the number of working men be x.
∴ M1D1 = M2D2
⇒ x × 60 = (x + 6) × 40
⇒ 3x = 2x + 12
⇒ 3x – 2x = 12
⇒ x = 12Correct Option: B
Let the number of working men be x.
∴ M1D1 = M2D2
⇒ x × 60 = (x + 6) × 40
⇒ 3x = 2x + 12
⇒ 3x – 2x = 12
⇒ x = 12
- A can do a piece of work in 10 days and B can do it in 12 days. They work together for 3 days. Then B leaves and A alone continues. 2 days after that C joins and the work is completed in 2 days more. In how many days can C do it, if he works alone ?
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Let C alone complete the work in x days.
According to the question, A’s 7 days’ work + B’s 3 days’ work + C’s 2 days’ work = 1⇒ 7 + 3 + 2 = 1 10 12 x ⇒ 2 = 1 - 7 - 1 x 10 4 = 20 - 14 - 5 = 1 20 20
⇒ x = 2 × 20 = 40 daysCorrect Option: C
Let C alone complete the work in x days.
According to the question, A’s 7 days’ work + B’s 3 days’ work + C’s 2 days’ work = 1⇒ 7 + 3 + 2 = 1 10 12 x ⇒ 2 = 1 - 7 - 1 x 10 4 = 20 - 14 - 5 = 1 20 20
⇒ x = 2 × 20 = 40 days
- Ramesh and Rahman can do a work in 20 and 25 days respectively. After doing collectively for 10 days at the work, they leave the work due to illness and Suresh completes rest of the work in 3 days. How many days Suresh alone can take to complete the whole work ?
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Ramesh’s 1 day’s work = 1 20 Rahman’s 1 day’s work = 1 25 ∴ (Ramesh + Rahman)’s 1 days’ work = 1 + 1 20 25 = 5 + 4 = 9 100 100 ∴ Their 10 day‘s work = 1 - 9 = 1 10 10 ∵ Suresh does 1 work in 3 10
∴ Time taken by Suresh in doing 1 work = 3 × 10 = 30 daysCorrect Option: D
Ramesh’s 1 day’s work = 1 20 Rahman’s 1 day’s work = 1 25 ∴ (Ramesh + Rahman)’s 1 days’ work = 1 + 1 20 25 = 5 + 4 = 9 100 100 ∴ Their 10 day‘s work = 1 - 9 = 1 10 10 ∵ Suresh does 1 work in 3 10
∴ Time taken by Suresh in doing 1 work = 3 × 10 = 30 days
- Ram and Hari can cut 12 kgs nuts in 2 days. After 5 days, Hari left the work. Ram took 8 more days to cut the rest of the nuts. If total of 58 kgs of nuts were cut, the time taken by Hari to cut 10 kg of nuts is
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Nuts cut by Ram and Hari in 1 day = 12 kg = 6kg. .....(i) 2
Nuts cut by them in 5 days = 30 kg.
Amount of nuts cut by Ram alone = 58 – 30 = 28 kg.
Time = 8 days∴ Nuts cut by Ram in 1 day = 28 = 3.5 kg. 8
7there4; From equation (i),
Nuts cut by Hari in 1 day = (6 – 3.5) kg. = 2.5 kg.∴ Time taken by Hari in cutting 10 kg. of nuts = 10 = 4 days 2.5 Correct Option: D
Nuts cut by Ram and Hari in 1 day = 12 kg = 6kg. .....(i) 2
Nuts cut by them in 5 days = 30 kg.
Amount of nuts cut by Ram alone = 58 – 30 = 28 kg.
Time = 8 days∴ Nuts cut by Ram in 1 day = 28 = 3.5 kg. 8
7there4; From equation (i),
Nuts cut by Hari in 1 day = (6 – 3.5) kg. = 2.5 kg.∴ Time taken by Hari in cutting 10 kg. of nuts = 10 = 4 days 2.5
- A and B together can finish a work in 30 days. They worked on it for 20 days and then B left the work. The remaining work was done by A alone in 20 days more. In how many days can A alone finish the work?
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∴ (A + B)’s 20 days’ work = 1 30 (A + B)’s 1 day’s work = 20 = 2 30 3 Remaining work = 1 – 2 = 1 3 3 Time taken by A in doing = 1 of work = 20 days 3
∴ Time taken by A in doing whole work = 3 × 20 = 60 daysCorrect Option: D
∴ (A + B)’s 20 days’ work = 1 30 (A + B)’s 1 day’s work = 20 = 2 30 3 Remaining work = 1 – 2 = 1 3 3 Time taken by A in doing = 1 of work = 20 days 3
∴ Time taken by A in doing whole work = 3 × 20 = 60 days
