Time and Work
- Two workers A and B are engaged to do a piece of work. A working alone would take 8 hours more to complete the work than when work together. If B worked alone, would take
4 1 hours more than 2
when work together. The time required to finish the work together is
-
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Time taken by A and B = x hours (let).
∴ According to the question,
Time taken by A alone = (x + 8) hours.
Time taken by B alone= 
x + 9 
hours. 2 ∴ 1 + 1 = 1 x + 8 x + (9/2) x ∴ 1 + 1 = 1 x + 8 2x + 9 x = 2x + 9 + 2x + 16 = 1 (x + 8)(2x + 9) x = 4x + 25 = 1 2x2 + 16x + 9x +72 x
&rArrr; 4x2 + 25x = 2x2 + 25x + 72
⇒ 2x2 = 72⇒ x2 = 72 = 36 2
⇒ x =√36 = 6 hoursCorrect Option: D
Time taken by A and B = x hours (let).
∴ According to the question,
Time taken by A alone = (x + 8) hours.
Time taken by B alone= x + 9 hours. 2 ∴ 1 + 1 = 1 x + 8 x + (9/2) x ∴ 1 + 1 = 1 x + 8 2x + 9 x = 2x + 9 + 2x + 16 = 1 (x + 8)(2x + 9) x = 4x + 25 = 1 2x2 + 16x + 9x +72 x
&rArrr; 4x2 + 25x = 2x2 + 25x + 72
⇒ 2x2 = 72⇒ x2 = 72 = 36 2
⇒ x =√36 = 6 hours
- A can do 7/8 of work in 28 days, B can do 5/6 of the same work in 20 days. The number of days they will take to complete if they do it together is
-
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Using basics of Rule 2,
A does 7 work in 28 days. 8
∴ A will complete the work in28 × 8 = 32 days. 7 B does 5 work in 20 days. 6
∴ B will complete the work in20 × 6 = 24 days 5
∴ (A + B)’s 1 day’s work1 + 1 = 3 + 4 = 7 32 24 96 96
∴ Required time= 96 = 13 5 days 7 7 Correct Option: D
Using basics of Rule 2,
A does 7 work in 28 days. 8
∴ A will complete the work in28 × 8 = 32 days. 7 B does 5 work in 20 days. 6
∴ B will complete the work in20 × 6 = 24 days 5
∴ (A + B)’s 1 day’s work1 + 1 = 3 + 4 = 7 32 24 96 96
∴ Required time= 96 = 13 5 days 7 7
- A can do one and a half as much of a work which B can do in one day. B alone can do a piece of work in 18 days. They together can finish that work in
-
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Using basics of Rule 2,
Ratio of efficiency of A and B = 3 : 2
Ratio of time taken = 2 : 3
∴ Time taken by A= 2 × 18 = 12 days 3
∴ (A + B)’s 1 day’s work= 1 + 2 = 3 + 2 = 5 12 18 36 36
∴ Required time= 36 = 7 1 days. 5 5 Correct Option: D
Using basics of Rule 2,
Ratio of efficiency of A and B = 3 : 2
Ratio of time taken = 2 : 3
∴ Time taken by A= 2 × 18 = 12 days 3
∴ (A + B)’s 1 day’s work= 1 + 2 = 3 + 2 = 5 12 18 36 36
∴ Required time= 36 = 7 1 days. 5 5
- A does half as much work as B in one-third of the time taken by B. If together they take 10 days to complete a work, then the time taken by B alone to do it would have been
-
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Using basics of Rule 2,
If B completes a work in x days,
A will complete the same in2x days. 3 ∴ 1 + 3 = 1 x 2x 10 ⇒ 2 + 3 = 1 ⇒ 2x = 50 2x 10
⇒ x = 25 daysCorrect Option: B
Using basics of Rule 2,
If B completes a work in x days,
A will complete the same in2x days. 3 ∴ 1 + 3 = 1 x 2x 10 ⇒ 2 + 3 = 1 ⇒ 2x = 50 2x 10
⇒ x = 25 days
- A does half as much work as B in three- fourth of the time. If together they take 18 days to complete a work, how much time shall B take to do it alone?
-
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Using basics of Rule 2,
Let B completes the work in x days∴ Work done by A in 3x days 4 = 1 2
⇒ Time taken by A in completing the work= 2 × 3x = 3x days 4 2
∴ (A + B)’s 1 day’s work= 1 + 2 = 3 + 2 = 5 x 3x 3x 3x ∴ 5 = 1 ⇒ 3x = 90 3x 18
⇒ x = 30
Hence, time taken by B in completing the work = 30 daysCorrect Option: A
Using basics of Rule 2,
Let B completes the work in x days∴ Work done by A in 3x days 4 = 1 2
⇒ Time taken by A in completing the work= 2 × 3x = 3x days 4 2
∴ (A + B)’s 1 day’s work= 1 + 2 = 3 + 2 = 5 x 3x 3x 3x ∴ 5 = 1 ⇒ 3x = 90 3x 18
⇒ x = 30
Hence, time taken by B in completing the work = 30 days
