UPSC Aptitude-Numerical Contributed by Athira updated on Oct 2020
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UPSC CDS elementary mathematics,algebra stastitics solved question papers of previous years,UPSC CDS General awareness questions with answers and detailed explanations

1.      Find the H.C.F and L. C. M of x4y6z7  and x3y8z5 -----

(a)     x3y6z5,   x4y8z7        -      Ans
(b)     x4y6z7,   x3y8z5
(c)     x3y6z7,   x4y8z5
(d)     xy2z2,   x4y6z5

2.     If a Superfast train running at the rate of 120km per hour passes a bridge of 100metres long in 12 seconds, what is the length of the train ?
(a)     260 m
(b)     300 m       -     Ans
(c)     360 m
(d)     400 m
Expl : Distance covered by train in 12 seconds     =    120 * 5/18 * 12
=     400 m
:. Length of the train                                              =     400-100  = 300 m

3.     A tradesman marks his goods 30% above the C.P. If he allows discount of 6 and 1/4 %, then his gain percent is :
(a)     23  and 3/4 %
(b)     22 %
(c)     21 and 7/8%       -     Ans
(d)     None

Expl : Let CP. be Rs.100. Then, marked price = Rs.130
S.P. = (100 - 25)% of Rs.130=(375 x130) = 121.875
4                          400
:. Profit % = 21.875 = 21875  = 21 and 7/8 %
1000
4.     A sum of money becomes 8 times of itself in 3 years at compound interest. The rate of interest is :
(a)     100 %       -     Ans
(b)     8 %
(c)     1 %
Expl : P (  1+ R )3 = 8P   or (1+ R  )3 = 8 = 23
100                      100
:. 1+ R         = 2 or  R   = 1 or   R = 100
100                100

5.     A and B are two alloys of gold and copper prepared by mixing metals in the ratio 7:2 and 7:11 respectively. If equal quantities of the alloys are melted to form a third alloy C, the ratio of gold and copper in C will be :
(a)     5:9
(b)     5:7
(c)    7:5      -     Ans
(d)     9:5
Expl :  Gold in  C (7/9 + 7/18) = 7/6
Copper in C =  (2/9 + 11/18) = 5/6
Gold : Copper = 7/6 : 5/6 : = 7 : 5

6.     Three years ago the average age of A and B was 18 years. With C joining them now, the average becomes 22 years. How old is C now ?
(a)    24 years     -     Ans
(b)     27 Years
(c)     28 years
(d)     30 years
Expl : (A+B)'s age 3 years ago    = (18 x2) years = 36 years.
:. (A+B) now = (36+3+3+) years  = 42 years
(A+B+C) now = (22x3) years       = 66 years
:. C now = (66-42) years             = 24 years

7.     The value of (2n + 2n-1) is :
________
2n+1 2n
(a)      1/2
(b)     3/2         -     Ans
n-1
(c)    2 n+1
(d)     None of these

Expl: Given exp. =   2 n-1 (2+1)    3
_________  =
2 n(2-1)          2

8.    On dividing 4150 by a certain number, the quotient is 55 and the remainder is 25. The divisor is :

(a)   65
(b)   70
(c)   75   -     Ans
(d)   80
Expl : Divisor = (Dividend - Remainder)     =    (4150 - 25)  = 75
Quotient                        55
9.     0.000006723 when expressed in scientific notation, is :
(a)    6723 x 10 -5
(b)    67.23 x 10 -7
(c)    6.723 x 10 -6  -     Ans
(d)    None
Expl : 0.000006723 = 0.000006723 x 106 = 6.723     = 6.723x 10-6
106                   106

10.  A man distributed Rs.100 equally among his friends. If there had been 5 more friends, each would have received one rupee less. How many friends had he ?
(a)   20 -     Ans
(b)    25
(c)    30
(d)    35

Expl : Suppose he had x friends. Then,
100  -  100  = 1   or 1  -   1      =  1
x        x+5             x    x+5       100

x+5-x    = 1      or  x2+5x-500 = 0 or (x+25)(x-20) = 0
x(x+5)     100
:. x = 20

11.   ? 9.5 x .0085 x18.9   is equal to :
.0017 x 1.9 x 2.1
(a)    0.15
(b)    0.5
(c)    15    -     Ans
(d)    250
Expl : Given Exp = ? 95 x 85 x 189  =  ? 5x5x9   = 15
17 x 19 x 21

12. The sum of two numbers is twice their difference. If one of the numbers is 10, the other one is :
(a)     3 and 1/3
(b)     -3 and 1/3
(c)     4 and 1/4
(d)     30   -     Ans
Expl :
Let the other number be x. Then,
10 + x = 2 (x-10) => x = 30

13.     A cricket team won 40% of the total number of matches it played during a year. If it lost 50% if the matches played and 20 matches were drawn, the total number of matches played by the team during the year was :
(a)    200   -     Ans
(b)    100
(c)     50
(d)     40

Expl:     40 % of x + 50% of x + 20 = x
=>   40 x + 50x + 20 = x   or x =200
100     100

14.    A workers earn Rs.280 in 5 days working 8 hours per day. How much will 12 workers earn in 2 days working 4 hours per day ?
(a)     Rs.168   -     Ans
(b)     Rs.172
(c)     Rs.224
(d)     Rs.196

Expl : If a workers working 8 hours per day earn in 5 days Rs.280
:. I worker working 1 hour per day earn in 1 day    =   280
4x8x5
:.  12 workers working 4 hours per day earn in 2 days   =   280 x 12 x 4 x 2    = Rs.168
4 x 8 x 5

15.    A thief steals a car at 2.30 pm and drives it at 60 kmph. The theft is discovered at 3 pm, and the owner sets off in another car at 75 kmph. When will he overtake the thief?
(a)     4.30 p.m.
(b)     4.45 p.m.
(c)    5.00 p.m.   -     Ans
(d)     5.15 p.m.
Expl : Suppose the thief is overtaken x hrs after 2.30pm. Then, distance covered by the thief in x hrs.
=distance covered by the owner in (x-1/2)hrs
:. 60 x = 75(x-1/2) or 15x = 75/2 or x=5/2 hrs. ie., He is overtaken at 5 p.m.

16. A toothed wheel of diameter 50 cm is attached to a smaller wheel of diameter 30cm. How many revolutions will the smaller wheel make when the larger one makes 15 revolutions?
(a)    18
(b)    20
(c)    25  -     Ans
(d)    30
Expl : Distance moved by toothed wheel in

15 revolutions = (15x2x22/7x25)cm
Distance moved by smaller wheel in 1 revolution       = (2x22/7x15)cm
:. Required number of revolutions  = (15 x 44/7 x 25x       7     ) = 25
44 x 15
17. The number of rounds that a wheel of diameter 7/11m will make in going 4km, is :
(a)    1000
(b)    1500
(c)    1700
(d)    2000  -     Ans
Expl : Distance moved in 1 revolution = (2 x 22/7 x 7/22)m = 2m
Number of revolutions in going 4 km = (4 x 1000)   = 2000
2

18. A tap can fill a tank in 16 minutes and another can empty it in 8 minutes. If the tank is already half full and both tanks are opened together, the tank will be :
(a)    filled in 12 min.
(b)    emptied in 12 min.
(c)    filled in 8 min
(d)   emptied in 8 min     -     Ans
Expl : Rate of waste pipe being more, the tank will be emptied when both the pipes are opened
Net emptying work done by both in 1 min. = (1/8 - 1/16) = 1/16
Now, full tank will be emptied by them in 16 min.
:. Half full tank will be emptied in 8 min.
19.   The length of the longest rod that can be placed in a room 30m long, 24 m broad and 18m high, is :
(a)    30m
(b)    15?2m
(c)    30?2m      -     Ans
(d)     60 m
Expl : length of the longest rod = length of diagonal = ?l2 + b2+h2
= ?302 + 242 + 182 = ?1800 = 30?2 m

20.    A cube of side 6cm is cut into a number of cubes, each of side 2cm. The number of cubes will be :
(a)    6
(b)    9
(c)    12
(d)   27     -     Ans
Expl : Number of cubes = Volume of bigger cube   = (6 x6x6) = 27
Volume of smaller cube      2x2x2

21.    ABC is a triangle right-angled at C. If p is the length of the perpendicular from C to AB and a,b,c, are the sides, then which one of the following is correct ?
(a)    pa = bc
(b)    pb =ca
(c)   pc=ab     -     Ans
(d)    p2 =ab
Expl :

Area of  triangle ABC = 1/2 x b x a
= 1/2 x p x c
:.                pc  = ab

22.  What is the value of -------

(a)    2
(b)    >2
(c)   >2    -     Ans
(d)    <2

Directions (q.23.25) : The students of various classes of a school, are represented by the following Pie-chart.  Total number of students of the school is 1000. Answer each of the following questions on the basis of the pie-chart.

23. How many number of students of class VI is less than number of students of class IX ?
(a)    133
(b)    57
(c)    166
(d)   67 -     Ans
(e)    None of these
Expl : No of students in a class VI = 72 x 1000    = 200
360
and no of students of class IX = 96 x 1000    = 267
360
:. Reqd difference  = 267-200 = 67

24.   What is the ratio between the number of students of class X and the number of students of class VIII ?
(a)    2 :3
(b)    4:3
(c)    1:2
(d)    4:5
(e)    9:4  -     Ans
Expl : No of students in a class X = 108 x 1000    = 300
360
and no of students of class VIII = 48 x 1000    = 400
360               3
:. Reqd ratio  = 300 : 400/3   = 9:4
25.   How many per cent is the number of students of class VII to the total number of student of the school ?
(a)    36
(b)    71
(c)    25
(d)    10    -     Ans
(e)    None of these
Expl : No of students in a class VII = 36 x 1000    = 100
360

:. Reqd percentage = 100x100    = 10
1000