Time and Work
- A and B can do a work in 8 days. B alone can do it in 24 days. In how many days, A alone can do the same work?
-
View Hint View Answer Discuss in Forum
(A + B)’s 1 day’s work
= 1 8
B’s 1 day’s work= 1 24
∴ A’s one day’s work
= (A + B)’s one day’s work – B’s one day’s work= 1 - 1 = 3 - 1 = 1 8 24 24 12
∴ A will complete the work in 12 days.
Aliter : Using Rule 4,
Here, x = 24, y = 8
Required time= xy days x - y = 24 × 8 = 12 days 24 - 8 Correct Option: C
(A + B)’s 1 day’s work
= 1 8
B’s 1 day’s work= 1 24
∴ A’s one day’s work
= (A + B)’s one day’s work – B’s one day’s work= 1 - 1 = 3 - 1 = 1 8 24 24 12
∴ A will complete the work in 12 days.
Aliter : Using Rule 4,
Here, x = 24, y = 8
Required time= xy days x - y = 24 × 8 = 12 days 24 - 8
- A can do 1/2 of a work in 9 days while B can do 1/3 of the same work in 6 days. How long would it take for A and B together to complete the work?
-
View Hint View Answer Discuss in Forum
A’s 9 days’ work
= 1 2
∴ A’s 1 day’s work= 1 = 1 2 × 9 18 B’s 6 days’ work = 1 3
∴ B’s 1 day’s work= 1 = 1 3 × 6 18
∴ (A + B)’s 1 day’s work= 1 + 1 = 2 = 1 18 18 18 9
∴ A and B both together will
complete the work in 9 days.
Aliter : Using Rule 2,
A’s 1 day work= 1 = 1 days 2 × 9 18
Required time taken= x × y x + y = 18 × 18 18 + 18 = 18 × 18 = 9 days 36 Correct Option: B
A’s 9 days’ work
= 1 2
∴ A’s 1 day’s work= 1 = 1 2 × 9 18 B’s 6 days’ work = 1 3
∴ B’s 1 day’s work= 1 = 1 3 × 6 18
∴ (A + B)’s 1 day’s work= 1 + 1 = 2 = 1 18 18 18 9
∴ A and B both together will
complete the work in 9 days.
Aliter : Using Rule 2,
A’s 1 day work= 1 = 1 days 2 × 9 18
Required time taken= x × y x + y = 18 × 18 18 + 18 = 18 × 18 = 9 days 36
- If A alone can do a work in 12 days and B alone can do it in 8 days, Working together, in how many days will they complete it?
-
View Hint View Answer Discuss in Forum
A’s one day’s work = 1 12 B’s one day’s work = 1 8
(A + B)’s one day’s work= 1 + 1 = 2 + 3 = 5 12 8 24 24 Now, 5 work is done in1day 24 ∴ 1 work is done in = 24 days 5 = 4 4 days 5
Aliter : Using Rule 2,
Here, x = 12, y = 8
Required time taken= xy x + y = 12 × 8 = 24 12 + 8 5 = 4 4 days 5 Correct Option: A
A’s one day’s work = 1 12 B’s one day’s work = 1 8
(A + B)’s one day’s work= 1 + 1 = 2 + 3 = 5 12 8 24 24 Now, 5 work is done in1day 24 ∴ 1 work is done in = 24 days 5 = 4 4 days 5
Aliter : Using Rule 2,
Here, x = 12, y = 8
Required time taken= xy x + y = 12 × 8 = 24 12 + 8 5 = 4 4 days 5
- A contract is to be completed in 50 days and 105 men were set to work, each working 8 hours a day. After 25 days, 2/5 th of the work is finished. How many additional men be employed so that the work may be completed on time, each man now working 9 hours a day?
-
View Hint View Answer Discuss in Forum
⇒ 2 × 9 × x = 3 × 8 × 105 5 5 ⇒ 3 × 8 × 105 = 140 2 × 9
Number of additional men
= 140 – 105 = 35Correct Option: A
⇒ 2 × 9 × x = 3 × 8 × 105 5 5 ⇒ 3 × 8 × 105 = 140 2 × 9
Number of additional men
= 140 – 105 = 35
- Rita, Sita and Meeta are employed to do a piece of work for ₹625. Rita and Sita together are supposed to do 17/23 of the work. What should Meeta be paid?
-
View Hint View Answer Discuss in Forum
Using Rule 1,
Amount received by Meeta= 6 × 625 = Rs. 163.04 23 Correct Option: B
Using Rule 1,
Amount received by Meeta= 6 × 625 = Rs. 163.04 23
