Work and Time: SSC CGL Practice Questions

Ans: A

Explanation: Let’s denote the total work as the least common multiple of 12 and 18, which is 36 units. A’s work rate is 36/12 = 3 units/day, and B’s work rate is 36/18 = 2 units/day. In the first 4 days, A and B work together, completing 4 * (3 + 2) = 20 units of work. The remaining work is 36 – 20 = 16 units. Let C’s work rate be ‘c’ units/day. A and C work for 4 days and complete the remaining 16 units. Therefore, 4 * (3 + c) = 16. Solving for c, we get 3 + c = 4, so c = 1 unit/day. C can do the whole job in 36/1 = 36 days. Half the job is 36/2 = 18 units. Therefore, it would take C 18/1 = 18 days to do half the original job alone.

Correct Option: A

Ans: C

Explanation: A and B complete 3/5 of the task, so C completes 1 – 3/5 = 2/5 of the task. If the payment is shared equally, each person should be paid based on the work done by them. The payment is Rs. 5000. Assuming they share it equally, if work done is considered,
A: 3/5 * 5000 / 3/5+3/5+2/5 = 3/5 * 5000 / 8/5
B: 3/5 * 5000 / 3/5+3/5+2/5 = 3/5 * 5000 / 8/5
C: 2/5 * 5000 / 3/5+3/5+2/5 = 2/5 * 5000 / 8/5

The correct approach would be:
Since the payment is to be shared equally among A,B and C and total payment is Rs 5000,
If they all contribute equally then, each would receive 5000/3 = 1666.66 Rs
A and B do work = 3/5
C does work = 2/5
Assuming they share equally (5000/3), the question states how much C receives. C did 2/5 of the work and if shared equally, C would receive 5000/3 = 1666.66
This question is ambiguously worded, as it does not clearly specify that the payment is shared equally based on work done or if the payment is split equally between the 3 people.
If shared as per work, A and B receive 3/5 * (5000) *1/3/8/5 = 3/8*5000= 1875
If shared as per work, C receives 2/5 * (5000) *1/3/8/5 = 2/8*5000= 1250
If shared equally between all, each would receive 5000/3 = 1666.67
However the question asks how much money C receives and doesn’t specify if money is based on the task done.
If the amount is split evenly, C receives 5000/3, which is not an option.

If they share equally between themselves.
Let the amount each is supposed to be paid is x, since they share it between themselves, they are expected to do the work.
A + B share 3/5 work => payment to A + B is 3/5 * total amount.
C did 2/5 work => payment to C is 2/5 * total amount.

The question says C gets some amount.
If the question intends share equally among them. Total payment is Rs. 5000. If it is divided equally then
C gets 5000/3. Since this is not in the options and question is poorly constructed, the best approach is to consider as work done.

C’s portion = (2/5) of total payment = (2/5) * 5000 = 2000.
Correct Option: C

Ans: C

Explanation:
Let the total work be W.
A can complete the task in 48 days. So, A’s work per day = W/48.
The task is finished in 11 and 1/3 days = 34/3 days.
Since A and B work on alternate days starting with B, the number of days B works = (34/3 + 1)/2 = 18/3 = 6 if 34/3 is odd or (34/3)/2= 17/3 which is impossible since days have to be whole numbers .
Since B starts, there are 6 days where B works and 5 days where A works.
Work done by A in 5 days = 5 * (W/48) = 5W/48
Work done by B in 6 days = W – 5W/48 = 43W/48
B’s work per day = (43W/48) / 6 = 43W/288
So, B can complete the task in 288/43 days.
Time taken by B to complete 4 times the same task = 4 * (288/43) = 1152/43 days.
The nearest answer is probably off because of rounding due to alternating days. Let’s reconsider. 11 1/3 days is 34/3 days. Since B starts, he works for either 5 or 6 days.

Case 1: A works for 5 days and B for 6 days.
Work done by A in 5 days = 5 * (W/48) = 5W/48
Work done by B in 6 days: x * W / t , t being the time taken by B
Total work: 5W/48 + 6W/t = W
6/t = 1 – 5/48 = 43/48
t = 288/43 days.
Time taken by B to complete 4 times the task = 4 * 288/43 = 1152/43 = 26.79. Not possible.

A starts and works for 5 days. B for 6 days.
5(W/48) + 6X = W
6x= W – 5W/48= 43W/48
B per day: (43W/48)/6 = 43W/288
B can complete work in 288/43 days
4 tasks is: 4 * 288/43 = 1152/43 days.

In 34/3 days, B has worked 6 days and A has worked 5 days.
So work done = 5/48 + 6/x = 1 where x is the number of days B takes.
B’s total work = 6/x. A’s total work is 5/48.
6/x = 1 – 5/48 = 43/48
x = 6*48/43 = 288/43.
4 tasks take 4*288/43 = 1152/43 ~ 26.79
Let’s consider that the number of days A works = 5 days and the number of days B works = 6 days
5/48 + 6/B = 1;
6/B = 1-5/48
6/B = 43/48
B = 288/43.
4 tasks = 4*288/43 = 1152/43.

Assume total work is 1.
A’s 1-day work = 1/48
In 34/3 days, which is 11 and 1/3 days. The alternating days starting with B is:
Since days start with B. B-A-B-A-B-A-B-A-B-A-B
Days are 6B, 5A or 5B, 6A. Since it says finish, we choose 6B, 5A.
A did work for 5 days.
Work done by A = 5/48
Work done by B = 1-5/48 = 43/48
B does work for 6 days so B’s work per day is 43/48/6= 43/288. Therefore B can do work in 288/43 days.
To complete 4 times work:
4 * 288/43 = 1152/43 days. Which is close to 26.7 days.
The closest answer is 27.

Correct Option: C

Ans: B

Explanation: First, find how long A takes to complete the entire task. If A completes 1/5 of the task in 3 days, then A takes 3 * 5 = 15 days to complete the whole task. Next, find B’s work rate. B works at half the speed of A, meaning B takes twice as long as A to do the whole task. Therefore, B takes 15 * 2 = 30 days to complete the whole task. Now, find their combined work rate. In one day, A completes 1/15 of the task, and B completes 1/30 of the task. Working together, in one day they complete 1/15 + 1/30 = 2/30 + 1/30 = 3/30 = 1/10 of the task. They are asked to finish half the task which is 1/2 of the whole task. If they do 1/10 of the work per day, the number of days they take to complete the half task is (1/2) / (1/10) = (1/2) * (10/1) = 5 days.

Correct Option: B

Ans: B

Explanation: Let the work done by A, B, and C in one day be a, b, and c respectively.
We are given:
1. A and B complete the task in 40 days: 40(a + b) = 1 (Total work) => a + b = 1/40 …(1)
2. B and C complete the task in 36 days: 36(b + c) = 1 => b + c = 1/36 …(2)
3. A, B, and C complete the task in 24 days: 24(a + b + c) = 1 => a + b + c = 1/24 …(3)

From (1) and (3), we have:
(a + b) + c = 1/24
(1/40) + c = 1/24
c = 1/24 – 1/40 = (5 – 3)/120 = 2/120 = 1/60

From (2) and the value of c, we have:
b + c = 1/36
b + 1/60 = 1/36
b = 1/36 – 1/60 = (5 – 3)/180 = 2/180 = 1/90

Since B’s one-day work is 1/90, B would take 90 days to complete the task alone.

Correct Option: B

Ans: D

Explanation: Let the total work be W. P’s work rate is W/18 per day. In 5 days, P completes 5 * (W/18) = 5W/18 of the work. The remaining work is W – 5W/18 = 13W/18. P and Q together complete this remaining work in 2.6 days. Let Q’s work rate be R. The combined work rate of P and Q is (W/18 + R). Therefore, 2.6 * (W/18 + R) = 13W/18. Dividing both sides by 2.6, we get W/18 + R = 5W/18. Hence, R = 4W/18 = 2W/9. So, Q can complete the whole work in 9/2 = 4.5 days. 66.67% of the total work is (2/3)W. Time taken by Q to complete (2/3)W is (2/3)W / (2W/9) = (2/3) * (9/2) = 3 days.

Correct Option: D

Ans: D

Explanation: Let A’s work rate be 7x and B’s work rate be 5x. Together, their combined work rate is 7x + 5x = 12x. They complete the job in 17.5 days. The total work done can be considered as the combined work rate multiplied by the number of days, so the total work is 12x * 17.5 = 210x. B’s work rate is 5x. To find how long B takes to do the *whole* job, we divide total work by B’s work rate: 210x / 5x = 42 days. To find how long B takes to complete *half* of the job, we divide half the total work by B’s work rate: (210x / 2) / 5x = 105x / 5x = 21 days.

Correct Option: D

Ans: A

Explanation: Let’s denote the fractions of the tank filled or emptied per hour by pipes A, B, and C as 1/16, 1/24, and -1/x respectively.
Pipe A and B work from 10:30 AM to 8:30 PM, which is 10 hours. Pipe C works from 10:30 AM to 2:30 PM, which is 4 hours. The tank is full, so the combined work done is 1. We can represent this as an equation:
10(1/16) + 10(1/24) + 4(-1/x) = 1
5/8 + 5/12 – 4/x = 1
(15 + 10)/24 – 4/x = 1
25/24 – 4/x = 1
25/24 – 1 = 4/x
1/24 = 4/x
x = 4 * 24
x = 96
Correct Option: A

Ans: B

Explanation:
Let the efficiencies of A, B, and C be 7x, 5x, and 6x, respectively.
When working together, their combined efficiency is 7x + 5x + 6x = 18x.
They finish the job in 35 days, so the total work done is 18x * 35 = 630x.

B and C work together for 21 days. Their combined efficiency is 5x + 6x = 11x.
The work done by B and C in 21 days is 11x * 21 = 231x.
The remaining work is 630x – 231x = 399x.

A’s efficiency is 7x.
The number of days A needs to finish the remaining work is 399x / 7x = 57 days.

Correct Option: B

Ans: A

Explanation: First, find the work rate of each person. A’s work rate is 1/8, B’s is 1/10, and C’s is 1/12. Their combined work rate is (1/8) + (1/10) + (1/12) = (15 + 12 + 10)/120 = 37/120. The ratio of their work done is directly proportional to the amount they receive. Therefore, we can find the ratio of their individual contributions to the total work. B’s contribution to the total work is 1/10. The sum of the ratios is 1/8 + 1/10 + 1/12 = 37/120. B’s share = (B’s work / Combined work) * Total amount = (1/10) / (37/120) * 5550. However, the correct way is to find the ratio of their work done in terms of the total work i.e. 1/8:1/10:1/12. Which simplifies to 15:12:10. B’s share is therefore (12/(15+12+10)) * 5550 = (12/37) * 5550 = 1800.

Correct Option: A

Ans: A

Explanation: Let the volume of the tank be V.
Pipe A’s rate: V/72 per minute
Pipe B’s rate: V/90 per minute
Let C’s rate be -V/c per minute (since it empties the tank)
With all pipes open, the combined rate is: V/120 per minute
So, V/72 + V/90 – V/c = V/120
Dividing by V: 1/72 + 1/90 – 1/c = 1/120
1/c = 1/72 + 1/90 – 1/120 = (5 + 4 – 3)/360 = 6/360 = 1/60
So, C empties the tank in 60 minutes.
A and B work together for 12 minutes.
A’s work in 12 minutes = 12 * (V/72) = V/6
B’s work in 12 minutes = 12 * (V/90) = 2V/15 = 8V/60
Combined work of A and B in 12 minutes: V/6 + 2V/15 = 5V/30 + 4V/30 = 9V/30 = 3V/10.
The filled portion is 3/10 of the tank.
C empties the full tank in 60 minutes, so it empties 1/60 of the tank per minute.
Time taken by C to empty 3/10 of the tank = (3/10) / (1/60) = (3/10) * 60 = 18 minutes.

Correct Option: A

Ans: A

Explanation:
Let the total work be W.
The work done by 20 men in 1 day is W/30.
The work done by 1 man in 1 day is W/(30*20) = W/600.

In the first 10 days, 20 men worked. Work done in 10 days = 10 * (W/30) = 10 * (20 * W/600) = 200W/600 = W/3.
Remaining work = W – W/3 = 2W/3.

After 10 days, 5 men left, so 15 men worked. Let the number of days they worked be x.
Work done by 15 men in x days = 15 * x * (W/600) = xW/40.

5 men returned 5 days before the work was completed. So, 20 men worked for 5 days.
Work done by 20 men in 5 days = 5 * (W/30) = 5 * (20 * W/600) = 100W/600 = W/6.

Total work done = W/3 + xW/40 + W/6 = W
W/3 + W/6 + xW/40 = W
(1/3 + 1/6 + x/40) = 1
(1/2 + x/40) = 1
x/40 = 1 – 1/2 = 1/2
x = 40/2 = 20

Total number of days = 10 + x + 5 = 10 + 20 + 5 = 35 days.

Ans: A

Explanation: Let the total work be the Least Common Multiple (LCM) of 8 and 12, which is 24 units.
A’s work rate: 24/8 = 3 units/day
B’s work rate: 24/12 = 2 units/day
Let the total number of days taken to finish the work be ‘x’. A worked for (x-2) days. B worked for x days.
So, 3(x-2) + 2x = 24
3x – 6 + 2x = 24
5x = 30
x = 6
Correct Option: A

Ans: C

Explanation: Let’s represent the amount David is paid as ‘D’ and the amount Clara is paid as ‘C’. We know that C + D = $150. We also know that Clara types 60% of what David types, so C = 0.60D. Now we can substitute the second equation into the first: 0.60D + D = $150. Combining like terms, we get 1.60D = $150. Dividing both sides by 1.60, we find D = $150 / 1.60 = $93.75.

Ans: C

Explanation: First, calculate A’s daily wage: 80 rupees/hour * 8 hours/day = 640 rupees/day. Next, calculate B’s daily wage: 60 rupees/hour * 6 hours/day = 360 rupees/day. Finally, find the ratio of A’s daily wage to B’s daily wage: 640 : 360. Simplify the ratio by dividing both sides by their greatest common divisor, which is 40. This gives us 16 : 9.
Correct Option: C

Ans: D

Explanation: First find the work done by X in one day. X completes 3/7 of the project in 15 days, so X completes (3/7)/15 = 1/35 of the project in one day. The remaining project is 1 – 3/7 = 4/7. X and Y complete 4/7 of the project in 10 days, so they complete (4/7)/10 = 2/35 of the project in one day. Now, find Y’s work per day: (X+Y)’s work per day – X’s work per day = Y’s work per day, which is 2/35 – 1/35 = 1/35. Therefore, Y alone would take 1/(1/35) = 35 days to complete the entire project.