Time and Work
- Working 5 hours a day, A can complete a work in 8 days and working 6 hours a day, B can complete the same work in 10 days. Working 8 hours a day, they can jointly complete the work in
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Using Rule 2,
Working 5 hours a day, A can complete a work in 8 days.
i.e. A can complete the work in 40 hours.
Similarly,
B will complete the same work in 60 hours.
∴ (A + B)'s 1 hour’s work= 1 + 1 = 3 + 2 40 60 120 = 5 = 1 120 24
Hence, A and B together will complete the work in 24 hours.
∴ They can complete the work in 3 days working 8 hours a day.
Correct Option: A
Using Rule 2,
Working 5 hours a day, A can complete a work in 8 days.
i.e. A can complete the work in 40 hours.
Similarly,
B will complete the same work in 60 hours.
∴ (A + B)'s 1 hour’s work= 1 + 1 = 3 + 2 40 60 120 = 5 = 1 120 24
Hence, A and B together will complete the work in 24 hours.
∴ They can complete the work in 3 days working 8 hours a day.
- Two men undertake a job for ₹ 960. They can complete it in 16 days and 24 days respectively. They work along with a third man and take 8 days to complete it. Then the share of the third man should be
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Using Rule 25,
Work done by the third person in 1 day= 1 - 1 - 1 8 16 24 = 6 - 3 - 2 = 1 48 48
Ratio of their 1 day’s work= 1 : 1 : 1 = 3 : 2 : 1 16 24 48
∴ Share of the third person= 1 × 960 = 960 = ₹ 160 (3 + 2 + 1) 6 Correct Option: C
Using Rule 25,
Work done by the third person in 1 day= 1 - 1 - 1 8 16 24 = 6 - 3 - 2 = 1 48 48
Ratio of their 1 day’s work= 1 : 1 : 1 = 3 : 2 : 1 16 24 48
∴ Share of the third person= 1 × 960 = 960 = ₹ 160 (3 + 2 + 1) 6
- If there is a reduction in the number of workers in a factory in the ratio 15 : 11 and an increment in their wages in the ratio 22 : 25, then the ratio by which the total wages of the workers should be decreased is
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Using Rule 25,
Required ratio
= 15 × 22 : 11 × 25 = 6 : 5Correct Option: A
Using Rule 25,
Required ratio
= 15 × 22 : 11 × 25 = 6 : 5
- Stanie and Paul take a piece of work for ₹ 28,800. One alone could do it in 36 days, the other in 48 days. With the assistance of an expert, they finish it in 12 days. How much remuneration the expert should get ?
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Expert’s 1 day’s work
= 1 - 1 - 1 12 36 48 = 12 - 4 - 3 = 5 144 144
∴ Ratio of their respective work for 1 day= 1 : 1 : 5 = 4 : 3 : 5 36 48 144
∴ Expert’s share= 5 × 28800 = ₹ 12000 12 Correct Option: D
Expert’s 1 day’s work
= 1 - 1 - 1 12 36 48 = 12 - 4 - 3 = 5 144 144
∴ Ratio of their respective work for 1 day= 1 : 1 : 5 = 4 : 3 : 5 36 48 144
∴ Expert’s share= 5 × 28800 = ₹ 12000 12
- A and B were assigned to do a job for an amount of ₹ 1,200. A alone can do it in 15 days, while B can do it in 12 days. With the help of C, they can finish in 5 days. The share of amount that C earns is
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Using Rule 25,
According to the question,1 + 1 + 1 = 1 15 12 C 5 Let C's work in day be 1 C ⇒ 1 = 1 - 1 - 1 C 5 15 12 = 12 - 4 - 5 = 1 60 20 ∴ A : B : C = 1 : 1 : 5 = 4 : 5 : 3 15 12 20
∴ C’s share= 3 × 1200 = ₹ 300 12 Correct Option: A
Using Rule 25,
According to the question,1 + 1 + 1 = 1 15 12 C 5 Let C's work in day be 1 C ⇒ 1 = 1 - 1 - 1 C 5 15 12 = 12 - 4 - 5 = 1 60 20 ∴ A : B : C = 1 : 1 : 5 = 4 : 5 : 3 15 12 20
∴ C’s share= 3 × 1200 = ₹ 300 12
