UPSC Aptitude questions and answers
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 %
(d) Data inadequate
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 acertain 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 or1 - 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. â 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 = â 95 x 85 x 189 = â 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) 15â2m
(c) 30â2m - Ans
(d) 60 m
Expl : length of the longest rod = length of diagonal = âl2 + b2+h2
= â302 + 242 + 182 = â1800 = 30â2 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.png)
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
