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
54 – 34 = (52 + 32)(5 + 3)(5 – 3) = 34 x 8 x 2 which is divisible by 8
Let a = 7 and b = 5
74 – 54 = (72 + 52)(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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