Time and Work: SSC CGL Exam

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: 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.

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.