Time and Work
- Kamal can do a work in 15 days. Bimal is 50 per cent more efficient than Kamal in doing the work. In how many days will Bimal do that work?
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Using Rule 15,
Efficiency and time taken are inversely proportional Bimal : Kamal = 150 : 100 (work)
⇒ 100 : 150 (Time) = 2 : 3
∵ 3 units ⇒ 15 days∴ 2 units 15 × 2 = 10 3
Hence, Bimal complete the work in 10 daysCorrect Option: C
Using Rule 15,
Efficiency and time taken are inversely proportional Bimal : Kamal = 150 : 100 (work)
⇒ 100 : 150 (Time) = 2 : 3
∵ 3 units ⇒ 15 days∴ 2 units 15 × 2 = 10 3
Hence, Bimal complete the work in 10 days
- A does 20% less work than B. If A can complete a piece of work in
7 1 hours, then B can do it in 2
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A does 20% less work than B.
∴ Ratio of time taken = 5 : 4A completes a work in 15 hours 2
∴ Time taken by B to do the same work15 × 4 = 6 hours. 2 5 Correct Option: B
A does 20% less work than B.
∴ Ratio of time taken = 5 : 4A completes a work in 15 hours 2
∴ Time taken by B to do the same work15 × 4 = 6 hours. 2 5
- A is thrice as good a workman as B and is, therefore, able to finish a piece of work in 60 days less than B. The time (in days) in which they can do it working together is
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Using Rule 2,
If A completes the work in x days, B will do the same in 3x days.
∴ 3x – x = 60
⇒ 2x = 60
⇒ x = 30 and 3x = 90
∴ (A + B)’s 1 day’s work= 1 + 1 = 3 + 1 30 90 90 4 = 2 90 45
∴ A and B together will do the work in45 or 22 1 2 2 Correct Option: B
Using Rule 2,
If A completes the work in x days, B will do the same in 3x days.
∴ 3x – x = 60
⇒ 2x = 60
⇒ x = 30 and 3x = 90
∴ (A + B)’s 1 day’s work= 1 + 1 = 3 + 1 30 90 90 4 = 2 90 45
∴ A and B together will do the work in45 or 22 1 2 2
- A is 50% as efficient as B. C does half of the work done by A and B together. If C alone does the work in 20 days, then A, B and C together can do the work in
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If B alone completes the work in x days, A will do the same in 2x days
∴ (A + B)’s 1 day’s work1 + 1 = 2 + 1 = 3 x 2x 2x 2x and C’s 1 day’s work = 3 4x ∴ 3 = 1 4x 20
⇒ 4x = 3 × 20⇒ x = 3 × 20 = 15 4
∴ (A + B + C)’s 1day’s work= 1 + 1 + 3 2x x 4x = 1 + 1 + 1 30 15 20 = 2 + 4 + 3 = 9 = 3 60 60 20
Hence, all three together will complete the work in20 or 6 2 days 3 3 Correct Option: B
If B alone completes the work in x days, A will do the same in 2x days
∴ (A + B)’s 1 day’s work1 + 1 = 2 + 1 = 3 x 2x 2x 2x and C’s 1 day’s work = 3 4x ∴ 3 = 1 4x 20
⇒ 4x = 3 × 20⇒ x = 3 × 20 = 15 4
∴ (A + B + C)’s 1day’s work= 1 + 1 + 3 2x x 4x = 1 + 1 + 1 30 15 20 = 2 + 4 + 3 = 9 = 3 60 60 20
Hence, all three together will complete the work in20 or 6 2 days 3 3
- A and B together can do a work in 12 days. B and C together do it in 15 days. If A’s efficiency is twice that of C, then the days required for B alone to finish the work is
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(A + B)’s 1 day’s work
= 1 .............(i) 12
(B + C)’s 1 day’s work= 1 .............(ii) 15
∴ Difference between A and C’s 1 day’s work1 - 1 = 5 - 4 = 1 12 15 60 60
If A alone completes the work in x days, C will do the same in 2x days.∴ 1 - 1 = 1 x 2x 60 ⇒ 2 - 1 = 1 2x 60 ⇒ 1 = 1 2x 60
⇒ x = 30
∴ B’s 1 day’s work= 1 - 1 [From equation (i)] 12 30 = 5 - 2 = 3 = 1 60 60 20
Hence, B alone will complete the work in 20 days.Correct Option: C
(A + B)’s 1 day’s work
= 1 .............(i) 12
(B + C)’s 1 day’s work= 1 .............(ii) 15
∴ Difference between A and C’s 1 day’s work1 - 1 = 5 - 4 = 1 12 15 60 60
If A alone completes the work in x days, C will do the same in 2x days.∴ 1 - 1 = 1 x 2x 60 ⇒ 2 - 1 = 1 2x 60 ⇒ 1 = 1 2x 60
⇒ x = 30
∴ B’s 1 day’s work= 1 - 1 [From equation (i)] 12 30 = 5 - 2 = 3 = 1 60 60 20
Hence, B alone will complete the work in 20 days.
