Time and Work
- A can do a work in 5 days less than the time taken by B to do it. If both of them together take
11 1 9
days, then the time taken by ‘B’ alone to do the same work (in days) is
-
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Using Rule 2,
If the time taken by B to complete the work be x days, then
time taken by A = (x – 5) days∴ 1 + 1 = 9 x x - 5 100 ⇒ x - 5 + x = 9 x(x - 5) 100
⇒ 9x2 – 45x = 200x –500
⇒ 9x2 – 245x + 500 = 0
⇒ 9x2 – 225x – 20x + 500 = 0
⇒ 9x (x – 25) – 20 (x – 25) = 0
⇒ (x – 25) (9x – 20) = 0⇒ x = 25 because x ≠ 20 9 Correct Option: C
Using Rule 2,
If the time taken by B to complete the work be x days, then
time taken by A = (x – 5) days∴ 1 + 1 = 9 x x - 5 100 ⇒ x - 5 + x = 9 x(x - 5) 100
⇒ 9x2 – 45x = 200x –500
⇒ 9x2 – 245x + 500 = 0
⇒ 9x2 – 225x – 20x + 500 = 0
⇒ 9x (x – 25) – 20 (x – 25) = 0
⇒ (x – 25) (9x – 20) = 0⇒ x = 25 because x ≠ 20 9
- A can do a work in 21 days. B is 40% more efficient than A. The number of days required for B to finish the same work alone is
-
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Time taken by B
= 21 × 100 = 15 days 140
Aliter : Using Rule 17,
Here, x = 21, R = 40%
Time taken By B= x × 100 days 100 + R = 21 × 100 = 15 days 140 Correct Option: C
Time taken by B
= 21 × 100 = 15 days 140
Aliter : Using Rule 17,
Here, x = 21, R = 40%
Time taken By B= x × 100 days 100 + R = 21 × 100 = 15 days 140
- Pratibha is thrices as efficient as Sonia and is therefore able to finish a piece of work in 60 days less than Sonia. Pratibha and Sonia can individually complete the work respectively in
-
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Time taken by Sonia = 3x days (let)
∴ Time taken by Pratibha = x days
∴ 3x – x = 60 ⇒ 2x = 60
⇒ x = 30 days
∴ Time taken by Sonia
= 3x days = 3 × 30 = 90 days.Correct Option: C
Time taken by Sonia = 3x days (let)
∴ Time taken by Pratibha = x days
∴ 3x – x = 60 ⇒ 2x = 60
⇒ x = 30 days
∴ Time taken by Sonia
= 3x days = 3 × 30 = 90 days.
- A is thrice as good a workman as B and therefore is able to finish a job in 40 days less than B. Working together, they can do it in
-
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Using Rule 2,
Time taken by A to complete the work = x days
∴ Time taken by B to complete the work = 3x days
So, 3x – x = 2x = 40
⇒ x = 20 and 3x = 60
∴ (A + B)’s 1 day’s work= 1 + 1 = 3 + 1 20 60 60 = 4 = 1 60 15
∴ A and B together will complete the work in 15 daysCorrect Option: D
Using Rule 2,
Time taken by A to complete the work = x days
∴ Time taken by B to complete the work = 3x days
So, 3x – x = 2x = 40
⇒ x = 20 and 3x = 60
∴ (A + B)’s 1 day’s work= 1 + 1 = 3 + 1 20 60 60 = 4 = 1 60 15
∴ A and B together will complete the work in 15 days
- A takes twice as much time as B and thrice as much as C to complete a piece of work. They together complete the work in 1 day. In what time, will A alone complete the work.
-
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Let time taken by C to complete the work = x days
∴ Time taken by A to complete the work = 3x days
and time taken by B to complete the work= 3x days 2
According to the question,1 + 1 + 1 = 1 3x 3x x 2 ⇒ 1 + 2 + 1 = 1 3x 3x x ⇒ 1 + 2 + 3 = 1 3x ⇒ 6 = 1 ⇒ 2 = 1 3x x
⇒ x = 2
∴ Time taken by A
= 3x = 3 × 2 = 6 daysCorrect Option: C
Let time taken by C to complete the work = x days
∴ Time taken by A to complete the work = 3x days
and time taken by B to complete the work= 3x days 2
According to the question,1 + 1 + 1 = 1 3x 3x x 2 ⇒ 1 + 2 + 1 = 1 3x 3x x ⇒ 1 + 2 + 3 = 1 3x ⇒ 6 = 1 ⇒ 2 = 1 3x x
⇒ x = 2
∴ Time taken by A
= 3x = 3 × 2 = 6 days
