**Time and Work Questions for SSC-CPO Set-3 PDF**

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**Question 1: **A drum of kerosene is $\frac{3}{4}$ full. When 30 litres of kerosene is drawn from it, it remains $\frac{1}{2}$ full. The capacity of the drum is

a) 120 litres

b) 135 litres

c) 150 litres

d) 180 litres

**Question 2: **By what least number should 675 be multiplied so as to obtain a perfect cube number ?

a) 3

b) 5

c) 24

d) 40

**Question 3: **$0.\overline{001}$ is equal to

a) 1/1000

b) 1/999

c) 1/99

d) 1/9

**Question 4: **$\frac{4.41 \times 0.16}{2.1 \times 1.6 \times 0.21}$ is equal to

a) 1

b) 0.1

c) 0.01

d) 10

**Question 5: **If a and b are two odd positive integers, by which of the following integers is $(a^4-b^4)$ always divisible ?

a) 3

b) 6

c) 8

d) 12

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**Question 6: **$\frac{256 \times 256 – 144 \times 144}{112}$ is equal to

a) 420

b) 400

c) 360

d) 320

**Question 7: **Buses start from a bus terminal with a speed of 20 km/hr at intervals of 10 minutes. What is the speed of a man coming from the opposite direction towards the bus terminal if he meets the buses at intervals of 8 minutes ?

a) 3 km/hr

b) 4 km/hr

c) 5 km/hr

d) 7 km/hr

**Question 8: **A and B together can do a piece of work in 9 days. If A does thrice the work of B in a given time, the time A alone will take to finish the work is

a) 4 days

b) 6 days

c) 8 days

d) 12 days

**Question 9: **If $a^3+\frac{1}{a^3}=2$, then value of $\frac{a^2+1}{a}$ is (a is a positive number)

a) 1

b) 2

c) 3

d) 4

**Question 10: **The mean of 100 observations was calculated as 40. It was found later on that one of the observations was misread as 83 instead of 53. The correct mean is:

a) 39

b) 39.7

c) 40.3

d) 42.7

**Question 11: **The time taken by a train 160 m long, running at 72 km/hr, in crossing an electric pole is

a) 8 sec

b) 9 sec

c) 6 sec

d) 4 sec

**Question 12: **A and B start running at the same time and from the same point around a circle. If A can complete one round in 40 seconds and B in50 seconds, how many seconds will they take to reach the starting point simultaneously?

a) 10

b) 200

c) 90

d) 2000

**Question 13: **In what time will a 100 metre long train running with a speed of 50 km/hr cross a pillar

a) 7.0 sec

b) 72 sec

c) 7.2 sec

d) 70 sec

**Question 14: **A gun is fired at a distance of 6.64 km away from Ram. He hears the sound 20 seconds later. Then the speed of sound is

a) 664 m/s

b) 664 km/s

c) 332 m/s

d) 332 km/s

**Question 15: **A train leaves a station A at 7 am and reaches another station B at 11 am. Another train leaves B at 8 am and reaches A at 11.30 am. The two trains cross one another at

a) 8:36 am

b) 8:56 am

c) 9:00 am

d) 9:24 am

**Question 16: **A can do a piece of work in 4 days and B can do it in 12 days. In how many days will they finish the work, both working together ?

a) 4 days

b) 6 days

c) 2 days

d) 3 days

**Question 17: **A can do 1/4 of a work in 10 days. B can do 1/3 of the work in 20 days. In how many days can both A and B together do the work ?

a) 30 days

b) 32 days

c) 24 days

d) 25 days

**Question 18: **A and B can together finish a work in 30 days. They worked at it for 20 days and then B left. The remaining work was done by A alone in 20 more days.A alone can finish the work in

a) 60 days

b) 54 days

c) 48 days

d) 50 days

**Question 19: **P can do a piece of work in 9 days. Q is 50% more efficient than P. The number of days it takes for Q to do the same piece of work is

a) $3$

b) $13\frac{1}{2}$

c) $4\frac{1}{2}$

d) $6$

**Question 20: **Sixteen men can complete a work in fifteen days, twenty-four children can do the same work in twenty days. In how many days will eight men and eight children, complete the same work ?

a) $18$ days

b) $16 days$

c) $13\frac{1}{3}$ days

d) $20$ days

**Answers & Solutions:**

**1) Answer (A)**

Drum is $\frac{3}{4}$ full.

When 30 liters are drawn out of it, it becomes $\frac{1}{2}$ full.

Therefore $\frac{3}{4}$ – $\frac{1}{2}$ of drum = 30

$\frac{1}{4}$ of drum = 30

Total capacity of drum = 30 $\times$ 4 = 120 litres

**2) Answer (B)**

Factorising 675 we get

675 = 5 $\times$ 5 $\times$ 3 $\times$ 3 $\times$ 3

There in order to make 675 a perfect cube, it has to be multiplied by 5.

**3) Answer (B)**

Let $x =0.\overline{001}$ be the first equation

$1000x = 1000 \times 0.\overline001$

= $1.\overline{001}$

Let $1000x = 1.\overline{001}$ be second equation

Subtracting equation 1 from 2

$999x = 1$

$ x = \frac{1}{999}$

**4) Answer (A)**

$\frac{4.41 \times 0.16}{2.1 \times 1.6 \times 0.21}$

= $\frac{{2.1}^2 \times 0.16}{2.1 \times 0.16 \times 10 \times 0.21}$

=$\frac{{2.1}^21 \times 0.16}{2.1 \times 0.16 \times 2.1}$

=$\frac{{2.1}^2 \times 0.16}{{2.1}^2 \times 0.16}$

=1

**5) Answer (C)**

$(a^4-b^4) = (a^2+b^2)\times(a^2-b^2)$

= $(a^2+b^2)\times(a+b)\times(a-b)$

Let a = 5 , b= 3

5^{4 }– 3^{4} = (5^{2} + 3^{2})(5 + 3)(5 – 3) = 34 x 8 x 2 which is divisible by 8

Let a = 7 and b = 5

7^{4} – 5^{4 }= (7^{2} + 5^{2})(7 + 5)(7 – 5) = 74 x 12 x 2 which is also divisible by 8

**6) Answer (B)**

$\frac{256 \times 256 – 144 \times 144}{112} = \frac{256^2 – 144^2}{112} = \frac{(256 – 144)(256 + 144)}{112} = \frac{(112)(400)}{112} = 400$

**7) Answer (C)**

Distance between buses will $20\times\frac{10}{60}$ = $\frac{10}{3}$ km.

Now man is travelling this distance in 8 min. with the relative speed of (20+$x$) (let’s assume speed of man is $x$ km/hr )

hence (20+$x$) = $\frac{\frac{10}{3}}{\frac{8}{60}}$

$x$= 5

**8) Answer (D)**

A does thrice the work of B in a given time.

Let B’s efficiency = $x$ units/day

=> A’s efficiency = $3x$ units/day

Thus, (A+B)’s 1 day’s work = $x+3x=4x$ units/day

=> Total work done by them in 9 days = $4x \times 9=36x$ units

$\therefore$ Time taken by A alone to finish the work = $\frac{36x}{3x}=12$ days

=> Ans – (D)

**9) Answer (B)**

Given : $a^3+\frac{1}{a^3}=2$

To find : $\frac{a^2+1}{a}=(a+\frac{1}{a}) = x = ?$

We know that, $(a+\frac{1}{a})^3=a^3+\frac{1}{a^3}+3(a)(\frac{1}{a})(a+\frac{1}{a})$

=> $(a+\frac{1}{a})^3=2+3(a+\frac{1}{a})$

=> $x^3=2+3x$

=> $x^3-3x=2$

=> $x(x^2-3)=2 \times 1$

Thus, the only value that satisfy above equation is $x=2$

=> Ans – (B)

**10) Answer (B)**

Mean of 100 observations = 40

=> Sum of 100 observations = $100 \times 40=4000$

Now, replacing 53 instead of 83

=> Correct sum = $4000-83+53=3970$

$\therefore$ Correct mean = $\frac{3970}{100}=39.7$

=> Ans – (B)

**11) Answer (A)**

Speed of train = 72 km/hr

= $(72 \times \frac{5}{18})$ m/s = $20$ m/s

Length of train = 160 m

Using, time = distance/speed

=> Time taken = $\frac{160}{20}=8$ sec

=> Ans – (A)

**12) Answer (B)**

Time taken by A to complete 1 round = 40 seconds and by B = 50 seconds

=> Time taken by them to reach the starting point simultaneously = L.C.M.(40,50)

= 200 seconds

=> Ans – (B)

**13) Answer (C)**

Speed of train = 50 km/hr

= $(50 \times \frac{5}{18})$ m/s = $\frac{125}{9}$ m/s

Length of train = 100 m

Using, time = distance/speed

=> Time taken = $100\div \frac{125}{9}$

= $100 \times \frac{9}{125}$

= $\frac{36}{5}=7.2$ sec

=> Ans – (C)

**14) Answer (C)**

Distance of gun from Ram = 6.64 km = 6640 m

Time = 20 seconds

=> Speed of sound = distance/time

= $\frac{6640}{20}=332$ m/s

=> Ans – (C)

**15) Answer (D)**

Time taken by 1st train to travel from A to B = 11-7 = 4 hours

Time taken by 2nd train to travel from B to A = 11:30-8 = 3.5 hours

=> ratio of time taken by 1st train to 2nd train = $4 : \frac{7}{2}$ = 8 : 7

Since, speed is inversely proportion to time

=> Ratio of speeds of 1st train to 2nd train = 7 : 8

Let the speed of 1st train = $7x$ and 2nd train = $8x$ km/hr

Distance between the two stations = time * speed = $7x * 4 = 28x$ km

We know that, 1st train starts one hour early, thus it will cover $7x$ distance till the time 2nd train starts.

So, at 8.00 a.m., remaining distance between two trains = $28x-7x = 21x$ km

Also, the two trains are moving in opposite directions, =>relative speed of two trains = $8x+7x = 15$ km/hr

Now, time taken to meet = $\frac{21x}{15x} = \frac{7}{5}$ hours

=> $\frac{7}{5} * 60$ = 84 minutes after 8.00 a.m.

=> Time when they meet = 8.00 a.m. + 84 min = **9:24 a.m.**

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**16) Answer (D)**

A’s 1 day’s work=$\frac{1}{4}$

B’s 1 day’s work=$\frac{1}{12}$

(A+B)’s 1 day’s work=$\frac{1}{4}+\frac{1}{12}$

$=\frac{3+1}{12}$

$=\frac{4}{12}$

$=\frac{1}{3}$

$\therefore$ A and B together does the work in $3$ days.

Hence,Option D is correct.

**17) Answer (C)**

A does$\frac{1}{4}$ work in 10 days.

$\therefore$A will complete the work in $10\times4=40$ days.

Similarly, B will complete the work in $20\times3=60$ days.

(A+B)’s 1 day’s work=$\frac{1}{40}+\frac{1}{60}$

$=\frac{3+2}{120}$

$=\frac{1}{24}$

$\therefore$ time taken by A and B together to complete the work=$24$ days.

Hence, Correct option is C.

**18) Answer (A)**

(A+B)together do the work in 30 days.

$\therefore$ (A+B)’s 1 day’s work=$\frac{1}{30}$

$\therefore$ (A+B)’s 20 days’ work=$\frac{20}{30}$$=\frac{2}{3}$

Remaining Work=$1-\frac{2}{3}$

=$\frac{1}{3}$

$\because$ Time taken by A in doing $\frac{1}{3}$ work=20 days

$\therefore$ Time taken by A to complete the work=$20\times3$

=$60$days

Hence, Option A is correct.

**19) Answer (D)**

P can do a piece of work in 9 days.

let efficiency of p is 100%

then efficiency of Q will be 150%

let Q can do the same piece of work in x days.

work is constant. so

efficiency*no of days = constant

100*9 = 150*x

x = 6.

answer is option D.

**20) Answer (D)**

16 men can complete a work in 15 days

1 man can complete the work in (16*15) days

24 children can do the same work in 20 days

1 child can complete the work in (24*20) days

let x be the no.of days taken by 8 men and 8 children to complete the work, then

1/x = 8/(16*15) + 8/(24*20)

1/x = 1/30 + 1/60

1/x = 3/60

x = 20

answer is option D.

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