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1. A can do a piece of work in 10 days while B can do the same piece of work in 15 days. In how many days both will complete the same work together?
[a] 10 days
[b] 8 days
[c] 6 days
[d] 4 days
[e] None of these

A can do the work in 10 days
B can do the work in 15 days
Total work = 30 units
A can do 3 units per day
B can do 2 units per day
Together can can complete the work in = 30/5 = 6 days

2. A and B can do a piece of work in 18 days, B and C can do it in 24 days, A and C can do it in 36 days. In how many days C will complete the same work alone?
[a] 90 days
[b] 104 days
[c] 124 days
[d] 144 days
[e] None of these

A and B = 18 days
B and C = 24 days
A and C = 36 days
L.C.M of 18, 24 and 26 = 72
A and B = 72/18 = 4 days
B and C = 72/24 = 3 days
A and C = 72/36 = 2 days
2A+2B+2C = 9 days
A+B+C = 4.5 days
C alone can do it in= 4.5 - 4 = 0.5 days
Total work = 72/0.05 = 144 days

3. A can do a piece of work in 20 days and B can complete the same piece of work in 25 days. If they start the work together but after 6 days. A left the work. In how many days the total work would be finished?
[a] 22 days
[b] 19.5 days
[c] 17.5 days
[d] 14 days
[e] None of these

A = 20 days and B = 25 days
L.C.M = 100
A and B can work 9 units together
A and B worked for 6 days = 54 units work finished
remaining work = 100 - 54 = 46 units
C alone can finish 46 units in = 46/4 = 11.5 days
Total work finished in = 6 + 11.5 = 17.5 days

4. A and B and complete a piece of work in 24 days & 36 days respectively. They start the work but 3 days before completion of work, A left. In how many days will the total work be complete.
[a] 16.2 days
[b] 14 days
[c] 15.4 days
[d] 14.5 days
[e] None of these

A = 24 days and B = 36 days
L.C.M = 72
A can do = 3 units & B can do = 2 units
Last 3 days only B worked = 2 x 3 days = 6 units work completed
Remaining work = 66 units
66 units work was finished by A and B together
66/5 = 13.2
Total work finished in = 13.2 + 3 = 16.2

5. P and Q can complete a job in 24 days working together. P alone can complete it in 32 days. Both of them worked together for 8 days and then P left. The number of days Q will take to complete the remaining work is?
[a] 96 days
[b] 64 days
[c] 32 days
[d] 48 days
[e] None of these

P and Q = 24 days
P alone = 32 days
L.C.M = 96 units
P and Q can do = 4 units daily
Q alone can do = 1 units daily
P and Q worked together for 8 days = 4 x 8 = 32 units done
remaining units 96 - 32 = 64 units
remaining work will be completed by Q in
64/1 = 64 days

6. A can do a piece of work in 9 days and B can do the same piece of work in 12 days respectively. If they work for a day alternative, in how many days the work would be finished if A begins the work?
[a] 12 days
[b] 16.5 days
[c] 10.25 days
[d] 12.4 days
[e] None of these

A and B = 9 and 12 days respectively
Total work = 36 units
A on Day 1 = 4 units
B on Day 2 = 3 units
7 units in 2 days
35 units in 10 days
remaining work = 36 - 35 = 1
It's A turn to work = 1/4 = 0.25 days
So total work completed in 10 + 0.25 days = 10.25 days

7. Two workers A and B engaged to do a work. A working alone takes 8 hours more than to complete the job than if both work together, If B worked alone, he would need 4.5 hours more to complete the job, than they both working together. What time would they take to do the work together?
[a] 6 days
[b] 7.4 days
[c] 5 days
[d] 4.5 days
[e] None of these

Shortcut
√AB
√8x4.5
√36
6 days

8. A work is done by three person A, B and C. A alone takes 10 hours to complete the work but B and C working togeter takes 4 hours, for the completion of the same work. If all of them worked together and completed 14 times of the work, then how many hours have they worked?
[a] 12 hours
[b] 20 hours
[c] 40 hours
[d] 48 hours
[e] None of these

A can do in 10 hours , B and C can do in 4 hours
LCM = 20 units
A can do 2 units
B and C can do 5 units
All together they can do 7 units
14 time of work = 20 x 14 = 280 units
They will take = 280/7 = 40 hours

9. A, B and C can do a piece of work in 20, 25 and 30 days respectively. They started the work together after 2 days of start of work A quits and 3 days after A, B quits. In how many day the total work would be finished?
[a] 16 days
[b] 21 days
[c] 23 days
[d] 32 days
[e] None of these

A, B and C can do work in 20, 25 and 30 days
Total work = LCM of 20, 25 and 30 = 300
A can do = 15 units per day
B can do = 12 units per day
C can do = 10 units per day
together they can do 37 units per day
2 days after A left = 74 units work done
3 days after B left = 66 units work done
remaining 160 units
C can complete 160 units in = 160/10 = 16 days
So, No of days to complete the total work is 2 + 3 + 16 = 21 days

10. 30 Children can do a piece of work in 16 days. How many children would be required to do the same work in 20 days?
[a] 24 Children
[b] 21 Children
[c] 18 Children
[d] 28 Children
[e] None of these

30 can do work in 16 days
then work = 30 x 16 = 480
480 work can be completed by how many children in 20 days = 480/20 = 24 Children

IBPS Clerk 2019 | Time and Work | Maths | 03 Reviewed by Santhosh Nair on 7:49 PM Rating: 5