Time and Work
- A can do a piece of work in 6 days. B is 25% more efficient than A. How long would B alone take to finish this work?
-
View Hint View Answer Discuss in Forum
Ratio of A's and B's efficiency = 4 : 5
Ratio of time taken = 5 : 4∴ Time taken by B = 6 × 4 5 = 24 = 4 4 days 5 5
Aliter : Using Rule 17,
Here, x = 6, R = 25%
Time taken by B= x × 100 days 100 + R = 6 × 100 125 = 6 × 4 5 = 24 = 4 4 days 5 5 Correct Option: A
Ratio of A's and B's efficiency = 4 : 5
Ratio of time taken = 5 : 4∴ Time taken by B = 6 × 4 5 = 24 = 4 4 days 5 5
Aliter : Using Rule 17,
Here, x = 6, R = 25%
Time taken by B= x × 100 days 100 + R = 6 × 100 125 = 6 × 4 5 = 24 = 4 4 days 5 5
- To do a certain work, B would take time thrice as long as A and C together and C twice as long as A and B together. The three men together complete the work in 10 days. The time taken by A to complete the work separately is
-
View Hint View Answer Discuss in Forum
Using Rule 2 and 3,
If B does the work in 3x days, (A + C) will do the same work in xdays.
If C does that work in 2y days.(A + B) will do it in y days.1 + 1 = 1 x 3x 10 ∴ 4 = 1 3x 10
⇒ 3x = 40⇒ x = 40 3 Again, 1 + 1 = 1 y 2y 10 ⇒ 3 = 1 2y 10
⇒ y =15
∴ (A + B + C)’s 1 day’s work= 1 10 ⇒ 1 + 1 + 1 = 1 A 40 30 10 ⇒ 1 = 1 - 1 - 1 A 10 40 30 = 12 - 3 - 4 = 5 = 1 120 120 24
∴ A alone will complete the work in 24 days.Correct Option: B
Using Rule 2 and 3,
If B does the work in 3x days, (A + C) will do the same work in xdays.
If C does that work in 2y days.(A + B) will do it in y days.1 + 1 = 1 x 3x 10 ∴ 4 = 1 3x 10
⇒ 3x = 40⇒ x = 40 3 Again, 1 + 1 = 1 y 2y 10 ⇒ 3 = 1 2y 10
⇒ y =15
∴ (A + B + C)’s 1 day’s work= 1 10 ⇒ 1 + 1 + 1 = 1 A 40 30 10 ⇒ 1 = 1 - 1 - 1 A 10 40 30 = 12 - 3 - 4 = 5 = 1 120 120 24
∴ A alone will complete the work in 24 days.
- P is thrice as good a workman as Q and therefore able to finish a job in 48 days less than Q. Working together, they can do it in :
-
View Hint View Answer Discuss in Forum
Using Rule 2,
Let time taken by P = x days
Then, time taken by Q = 3x days
∴ 3x – x = 48 ⇒ x = 24
∴ (P + Q)’s 1 day’s work1 + 2 = 3 + 1 = 1 24 72 72 18
∴ Required time = 18 daysCorrect Option: A
Using Rule 2,
Let time taken by P = x days
Then, time taken by Q = 3x days
∴ 3x – x = 48 ⇒ x = 24
∴ (P + Q)’s 1 day’s work1 + 2 = 3 + 1 = 1 24 72 72 18
∴ Required time = 18 days
- A and B can do a job together in 12 days. A is 2 times as efficient as B. In how many days can B alone complete the work ?
-
View Hint View Answer Discuss in Forum
Using Rule 2,
If A alone completes the work in x days, B will complete the same in 2x days.∴ 1 + 1 = 1 x 2x 12 = 2 + 1 = 1 2x 12
⇒ 2x = 36
∴ B alone will complete the work in 36 days (i.e. 2x ).Correct Option: C
Using Rule 2,
If A alone completes the work in x days, B will complete the same in 2x days.∴ 1 + 1 = 1 x 2x 12 = 2 + 1 = 1 2x 12
⇒ 2x = 36
∴ B alone will complete the work in 36 days (i.e. 2x ).
- A can do a certain work in 12 days. B is 60% more efficient than A. How many days will B and A together take to do the same job?
-
View Hint View Answer Discuss in Forum
Time taken by B in completing the work
= 12 × 100 = 15 days 160 2
∴ (A+B)’s 1 day’s work1 + 2 = 5 + 8 = 13 12 15 60 60
Hence, the work will be completed in60 days 13
Aliter : Using Rule 17,
Here, x = 12, R = 60%
Time taken by B= x × 100 days 100 + R = 12 × 100 days 160 = 15 days 2
Now using Rule 2,
Time taken by A and B= xy x + y = 12 × 15 2 12 × 15 2 = 12 × 15 = 60 days 39 13 Correct Option: D
Time taken by B in completing the work
= 12 × 100 = 15 days 160 2
∴ (A+B)’s 1 day’s work1 + 2 = 5 + 8 = 13 12 15 60 60
Hence, the work will be completed in60 days 13
Aliter : Using Rule 17,
Here, x = 12, R = 60%
Time taken by B= x × 100 days 100 + R = 12 × 100 days 160 = 15 days 2
Now using Rule 2,
Time taken by A and B= xy x + y = 12 × 15 2 12 × 15 2 = 12 × 15 = 60 days 39 13
