Time And Work Problems For SSC CGL

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time and work problems for ssc cgl
time and work problems for ssc cgl

Time And Work Problems For SSC CGL

Download SSC CGL Time and Work Problems questions with answers PDF based on previous papers very useful for SSC CGL exams. 20 Very important Time and Work Problems on objective questions (MCQ’s) for SSC exams.

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Question 1: A person travelled from his home to his office at 48 km/hr and returned from his office to his home at 32 km/hr. Find his average speed.

a) 40 km/hr

b) 37.5 km/hr

c) 36 km/hr

d) 38.4 km/hr

Question 2: A train travelled from A to B at a speed of 60 km/hr and returned from B to A at a speed of 40 km/hr. Find the average speed of the train.

a) 50 km/hr

b) 48 km/hr

c) 42 km/hr

d) 56 km/hr

Question 3: The average speed of a bus is 72km/hr without stoppages and 60 km/hr with stoppages. How many minutes per hour does the bus stop.

a) 12 minutes

b) 10 minutes

c) 15 minutes

d) 16 minutes

Question 4: A train travels a certain distance in a certain time. If it covers triple the distance in double the time, then find the ratio between original speed and current speed.

a) 1:3

b) 2:3

c) 3:5

d) 2:5

Question 5: The average speed of a bus is 25 km/hr without stoppages and 20 km/hr with stoppages. How many minutes per hour does the bus stop?

a) 5 minutes

b) 20 minutes

c) 12 minutes

d) 15 minutes

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Question 6: A train travels from Delhi to Mumbai at a speed of 60 km/hr and returns at a speed of 75 km/hr. Find its average speed.

a) 66.67 km/hr

b) 45 km/hr

c) 60 km/hr

d) 67.5 km/hr

Question 7: A bus can travel at 150 km/hr without stoppages and at 120 km/hr with stoppages. How many minutes per hour does the bus stop?

a) 15 minutes

b) 12 minutes

c) 16 minutes

d) 20 minutes

Question 8: A train travels a distance of 480 km at uniform speed. Due to breakdown, its speed is reduced by 20 km/hr and hence it travels the destination 4 hours late. Find the initial speed of the train.

a) 60 km/hr

b) 40 km/hr

c) 25 km/hr

d) 35 km/hr

Question 9: A train travels at a speed of 125 km/hr without stoppages and at 100 km/hr with stoppages. How many minutes per hour does the train stop?

a) 25 min

b) 20 min

c) 15 min

d) 12 min

Question 10: A bus travels at a speed of 75 km/hr without stoppages and at 50 km/hr with stoppages. How many minutes per hour does the bus stop?

a) 25 min

b) 20 min

c) 15 min

d) 10 min

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Question 11: A, B and C can do a piece of work individually in 8, 12 and 4 days respectively. A started the work and is assisted by B and C on every third day. Then, in how many days will the work be completed?

a) $4\dfrac{1}{2}$ days

b) $5\dfrac{3}{4}$ days

c) $5\dfrac{1}{11}$ days

d) $4\dfrac{2}{3}$ days

Question 12: A, B and C can do a piece of work individually in 12, 16 and 24 days respectively. A started the work and is assisted by B and C on every third day. Then in how many days will the total work be completed?

a) $10\dfrac{1}{3}$ days

b) $8\dfrac{2}{3}$ days

c) $14$ days

d) $12$ days

Question 13: 20 men can complete a piece of work in 36 days. In how many days will 48 men with same efficiency be able to complete the work?

a) 12 days

b) 18 days

c) 15 days

d) 24 days

Question 14: A can do half of a piece of work in 12 days. B can do 1/4th of the same work in 12 days. In how many days will the total work be completed if they work together?

a) 14 days

b) 18 days

c) 12 days

d) 16 days

Question 15: A can do 1/3rd of the work in 10 days. B can do half of the same work in 15 days. In how many days will the work be completed if they both work together?

a) 12 days

b) 10 days

c) 15 days

d) 9 days

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Question 16: By working 8 hours a day, a man completed his work in 12 days. If the work needs to be completed in 8 days, then he needs to work for how many hours per day?

a) 10 hours

b) 12 hours

c) 14 hours

d) 16 hours

Question 17: A and B can do a piece of work individually in 24 days and 36 days respectively. A alone worked on it for 18 days and left. B can complete the remaining work in?

a) 12 days

b) 9 days

c) 6 days

d) 4 days

Question 18: A and B can do a piece of work individually in 20 days and 25 days respectively. A alone worked on it for 12 days and left. B can finish the remaining work in?

a) 9 days

b) 8 days

c) 10 days

d) 12 days

Question 19: A, B and C are employed to work for Rs.2100. A and B are supposed to finish $\dfrac{37}{42}th$ of work. Then, amount paid to C is?

a) Rs.225

b) Rs.300

c) Rs.325

d) Rs.250

Question 20: A, B and C are employed to do a work for Rs.1440. A and C are supposed to complete $\dfrac{29}{36}th$ of work. Then, Salary of B will be?

a) Rs.400

b) Rs.250

c) Rs.280

d) Rs.350

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Answers & Solutions:

1) Answer (D)

Let the distance between his home and his office be 96 km. (LCM of 48 and 32)
Total distance = 96+96 = 192 km
Time required to travel 96 km at 48 km/hr = 2 hours
Time required to travel 96 km at 32 km/hr = 3 hours
Total time = 2+3 = 5 hours
Average speed $= \dfrac{\text{Total Distance}}{\text{Total Time}} = \dfrac{192}{5} = 38.4 km/hr$

2) Answer (B)

Let the distance between A and B be 120 km each (LCM of 60 and 40).
Time taken by the train to travel 120 km at 60 km/hr = 2 hours
Time taken by the train to travel 120 km at 40 km/hr = 3 hours
Total distance = 120+120 = 240 km
Total time = 2+3 = 5 hours
Average speed $= \dfrac{\text{Total Distance}}{\text{Total Time}} = \dfrac{240}{5} = 48 km/hr$

3) Answer (B)

Due to stoppages, bus travelled 12 km less in an hour.
12 km can be travelled without stoppages in $\dfrac{12}{72} \times 60 = 10$ minutes

4) Answer (B)

Let the distance travelled by the train be D km.
Let the time taken by the train to travel D km be T hours.
Original speed = $\dfrac{D}{T}$ km/hr
New Distance = 3D km
New time = 2T hours
New speed = $\dfrac{3D}{2T}$ km/hr
Ratio between original speed and new speed = $\dfrac{D}{T} : \dfrac{3D}{2T} = 1 : \dfrac{3}{2} = 2:3$

5) Answer (C)

Due to stoppages, bus travelled 5 km less in an hour.
Time required to travel 5 km without stoppages = $\dfrac{5}{25} \times 60 = 12$ minutes

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6) Answer (A)

Let the total distance be 300 km (LCM of 60 and 75).
Time required to travel 300 km at 60 km/hr = 300/60 = 5 hours
Time required to travel 300 km at 75 km/hr = 300/75 = 4 hours
Total time to travel 600 km = 9 hours
Total distance = 600 km
Average speed = 600/9 = 200/3 = 66.67 km/hr

7) Answer (B)

Due to stoppages, bus travelled 30 km less in an hour.
Time taken to travel 30 km $= \dfrac{30}{150}\times60 = 12$ minutes

8) Answer (A)

Given that the distance $= 480$ km
Let the speed of the train $= x$ km/hr
Then, time in which it can travel $480$ km $= \dfrac{480}{x}$ hr
Now, Speed is reduced by $20$ km/hr
Reduced speed $= (x-20)$ km/hr
Time in which it can travel $480$ km at reduced speed $= \dfrac{480}{(x-20)}$
Difference in time = 4 hours
⇒ $\dfrac{480}{(x-20)} – \dfrac{480}{x} = 4$
⇒ $\dfrac{480(x-x+20)}{x^2-20x} = 4$
⇒ $9600 = 4(x^2-20x)$
⇒ $x^2-20x-2400 = 0$
⇒ $x^2-60x+40x-2400 = 0$
⇒ $x(x-60)+40(x-60) = 0$
⇒ $(x+40)(x-60) = 0$
x+40 = 0 | x-60 = 0
x = -40 | x = 60
Speeds cannot be negative.
Hence, Initial speed = 60 km/hr

9) Answer (D)

Due to stoppages, train travelled 25 km less in an hour.
Time required to travel 25 km in an hour $ = \dfrac{25}{125}\times 60 = 12$ minutes.

10) Answer (B)

Due to stoppages, bus travelled 25 km less in an hour.
Time required to travel 25 km in an hour $ = \dfrac{25}{75}\times 60 = 20$ minutes.

11) Answer (C)

Let the total work be 24 units.
Efficiency of A = 24/8 = 3 units/day
Efficiency of B = 24/12 = 2 units/day
Efficiency of C = 24/4 = 6 units/day
Given that A started the work and is assisted by B and C on every third day.
First day: 3 units
Second day: 3 units
Third day: 3+2+6 = 11 units
⇒ 17 units of work will be completed in 3 days.
Remaining work = 24-17 = 7 units
In 7 units, 6 units will be completed by A in 2 days.
Remaining 1 unit will be completed by A+B+C in $\dfrac{1}{6}$ days.
Hence, Total work will be completed in $3+2+\dfrac{1}{6} days = 5\dfrac{1}{6}$ days

12) Answer (B)

Let the total work be 48 units.
Efficiency of A = 48/12 = 4 units/day
Efficiency of B = 48/16 = 3 units/day
Efficiency of C = 48/24 = 2 units/day
A started the work and is assisted by B and C on every third day.

First day: 4 units
Second day: 4 units
Third day: 4+3+2 = 9 units
⇒ 17 units of work will be completed in 3 days.
⇒ 34 units of work will be completed in 6 days.
Remaining work = 48-34 = 14 units
8 units of work will be done by A in the next two days.
Remaining work = 14-8 = 6 units
6 units of work will be completed by A,B and C together in $\dfrac{6}{9} = \dfrac{2}{3}$ days
Hence, Total work will be completed in $6+2+\dfrac{2}{3} days = 8\dfrac{2}{3}$ days

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13) Answer (C)

$\text{No. of Men}_1 \times \text{No. of days}_1 = \text{No. of Men}_2 \times \text{No. of days}_2$
Let the number of days required be ‘x’
⇒ $20\times36 = 48\times x$
⇒ x = 15
Therefore, Number of days required for 48 men to complete the work = 15 days.

14) Answer (D)

Given, A can do half of the work in 12 days
⇒ A can do complete work in 24 days.
B can do 1/4th of the work in 12 days.
⇒ B can do complete work in 48 days.
Let the total work be 48 units (LCM of 24 and 48)
Efficiency of A = 48/24 = 2 units/day
Efficiency of B = 48/48 = 1 unit/day
Then, the total work will be completed in 48/3 = 16 days

15) Answer (C)

Given, A can do 1/3rd of work in 10 days
⇒ A can do complete work alone in 30 days
B can do half of work in 15 days
⇒ B can do complete work in 30 days
Let total work be 30 units (LCM of 30,30)
Efficiency of A = 30/30 = 1 unit/day
Efficiency of B = 30/30 = 1 units/day
Then, Total work will be completed in 30/2 = 15 days

16) Answer (B)

$\text{No. of hours}_1\times\text{No. of days}_1 = \text{No. of hours}_2\times\text{No. of days}_2$
Let the number of hours per day required to work to finish the work in 8 days = x hours
⇒ $8\times12 = 8\times x$
⇒ $x = 12$

17) Answer (B)

Let the total work be 72 units (LCM of 24 and 36).
Efficiency of A = 72/24 = 3 units/day
Efficiency of B = 72/36 = 2 units/day
A worked alone for 18 days.
A can do 3 units of work in a day.
⇒ In 18 days, he can complete 54 units of work.
Remaining work = 72-54 = 18 units
B can do 2 units of work in 1 day.
Then, 18 units will be completed by B in 18/2 = 9 days.

18) Answer (C)

Let the total work be 100 units (LCM of 20 and 25)
Efficiency of A = 100/20 = 5 units/day
Efficiency of B = 100/25 = 4 units/day
A worked alone for 12 days.
5 units of work will be completed by A in 1 day.
Then, 60 units of work will be completed by A in 12 days.
Remaining work = 100-60 = 40 units.
4 units of work will be completed by B in 1 day.
Hence, 40 units of work will be completed by B in 10 days.

19) Answer (D)

Let the total work be 42 units.
A and B will complete 37 units.
Remaining work = 42-37 = 55 units.
42 units → Rs.2100
1 unit → Rs.50
Then, Salary of C = 50*5 = Rs.250

20) Answer (C)

Let total work be 36 units.
A and C will complete 29 units.
Remaining work = 36-29 = 7 units.
36 units → Rs.1440
1 unit → Rs.40
Then, Salary of B will be 7*40 = Rs.280

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