Question 1
5% of 68.25 + 45% of 95% of 1755 = 35% of ? % of6350.
a) 33.91 b) 72.12 c) 23.91 d) 29.34
Answer : a) 33.91
Solution :
Given that, 5% of 68.25 + 45% of 95% of 1755 = 35% of ? % of 6350.
This can be written as, 5/100 x 68.25 + 45/100 x 95/100 x 1755 = 35/100 x ? /100 x 6350.
Converting the decimal 68.25 into fraction, we get
5/100 x 6825/100 + 45/100 x 95/100 x 1755 = 35/100 x ? /100 x 6350.
5x 6825/10000 + 45x 95/10000 x 1755 = 35 x ? /10000 x 6350
Cancelling out the denominator(10000) on both sides, we get
5 x 6825+ 45 x 95 x 1755 = 35 x ? x 6350
Dividing each term by 25 on both sides, we get
5 x 273 + 9 x 19 x 1755 = 35 x ? x 254
273 + 9 x 19 x 351 = 7 x ? x 254
60924 = 1778 x ?
? = 60924/1778 = 33.91
Hence the answer is 33.91.
Question 2
What % of 12% of 48.96 is the sum of 20% of 139.212 and 95% of 48.60?
a) 1151.74 b) 11517.4 c) 1259.74 d) 1957.74
Answer : c) 1259.74
Solution :
Given that, ? % of 12% of 48.96 = 20% of 139.212 + 95% of 48.60
The above eqn can be written as,
?/100 x 12/100 x 48.96 = 20/100 x 139.212 + 95/100 x 48.60
Converting the decimal numbers into fractions, we get
?/100 x 12/100 x 4896/100 = 20/100 x 139212/1000 + 95/100 x 4860/100
Cancelling out the denominators, we get
12 x ? / 10000 x 4896 / 100 = 2/10 x 139212/1000 + 95/100 x 4860/100
12x? x 4896/100 = 2 x 139212 + 95 x 4860
Divide both sides by 12,
? x 4896/100 = 2 x 11601 + 95 x 405
? x 4896/100 = (23202 + 38475)
? x 4896 = 6167700.
? = 6167700 / 4896 = 513975/408 = 1259.74
Hence, the required answer is 1259.74
Question 3
sqrt(1.44) % of sqrt(23.04) % of 1.5 % of 3125 = sqrt(?)% of 2.5920
a) 625/576 b) 576/529 c) 529/484 d) 484/441
Answer : a) 625/576.
Solution :
Given that, sqrt(1.44) % of sqrt(23.04) % of 1.5 % of 3125 = sqrt(?)% of 2.5920
Note that, sqrt(1.44) = 1.2 and sqrt(23.04) = 4.8
Put the above values in the given eqn,
1.2 % of 4.8 % of 1.5 % of 3125 = sqrt(?)% of 2.5920
1.2/100 x 4.8/100 x 1.5/100 x 3125 = sqrt(?)/100 x 2.5920
Convert decimal numbers into fractions,
12/1000 x 48/1000 x 15/1000 x 3125 = sqrt(?)/100 x 25920/10000
Cancel out the possible denominators on both sides,
12 x 48 x 15/1000 x 3125 = sqrt(?) x 25920
12 x 48 x 15 x 25 x 1/8 = sqrt(?) x 25920
15 x 25x 1/8 = sqrt(?)x 45
25/24 = sqrt(?)
? = (25/24)2 = 625/576.
Directions to solve :
In each of the number series question given below two terms have been placed within brackets. Mark
your answer as :
(a) If the first term in bracket is correct and second is wrong.
(b) If both the terms in bracket are correct.
(c) If the first term in bracket is wrong and the second is correct.
(d) If both the terms in bracket are wrong.
Question 4
65, (82), 101, 122, (146), 170.
Options : a, b, c, d.
Answer : option a.
Solution :
From the question, we can observe that the pattern used is X2 + 1 where
X = 8,9,10,11,12,…
That is, 82 + 1 = 64 + 1 = 65
92 + 1 = 81 + 1 = 82
102 +1 = 100 + 1
112 + 1 = 121 + 1 = 122
122 + 1 = 144 + 1 = 145
132 + 1 = 169 + 1 = 170.
Therefore, the first term in bracket is correct and the second one(146) is wrong.
Hence, the answer is option a.
Question 5
10, (16), 23, (35), 48, 65
Options : a, b, c, d.
Answer : option d.
Solution :
Go on adding 5, 8, 11, 14 and 17 to get the next number of series.
That is,
10 + 5 = 15
15 + 8 = 23
23 + 11 = 34
34 + 14 = 48
48 + 17 = 65
So, the numbers 16 and 35 are wrong.
Hence the answer is option d.
Question 6
17, 37, (77), 157, (317), 637.
Options : a, b, c, d.
Answer : option b.
Solution :
Each number of given series is twice the preceding one plus 3.
That is,
17 x 2 + 3 = 34 + 3 = 37
37 x 2 + 3 = 74 + 3 = 77
77 x 2 + 3 = 154 + 3 = 157
157 x 2 + 3 = 314 + 3 = 317
317 x 2 + 3 = 634 + 3 = 637
Therefore, the number 77 is correct and 317 is wrong.
Hence, the answer is a.
Question 7
If the radius of a cone is multiplied by 1/3 and height of the cone is tripled then the volume of new cone:
a) increases by one fourth b) increases by one third c) remains the same d) decreases thrice
Answer : b) increases by one third
Solution :
Let h and r be the height and radius of the cone
Then 3h and r/3 are the height and radius of new cone respectively.
We know that, the volume of a right circular cone of height h and radius r is 1/3 (pi)(r2)h unit3.
Now, the volume of the cone = 1/3 (pi) (r2)h.
Volume of new cone = 1/3 (pi) (r / 3)2 (3h) = 1/9 (pi) (r2) h
= 1/3 (1/3 (pi) (r2)h) = 1/3 x volume of of the cone.
Hence the answer is option b.
Question 8
If 3:2 is the ratio of radius of two right circular cones and 1:1 is the ratio of their volumes. Then what will
be the ratio of their heights ?
a) 1:3 b) 2:3 c) 7:2 d) 4:9
Answer : d) 4:9
Solution:
Ratio of radius = 3:2
Let their radius be 3X and 2X.
And 1:1 is the ratio of their volume which means they have equal volume.
Let h and H be their respective heights.
Then, (1/3) (pi) (3X)2 (h) = (1/3) (pi) (2X)2 (H)
9X2 (h) = 4X2 (H)
h / H = 4 / 9.
Hence required ratio is 4:9.
Question 9
If 1:2 and 1:3 are the ratios of radius and height of two different cones then which of the following is the
ratio of their volumes?
a) 1:1 b) 2:3 c) 1:12 d) 1:3
Answer : c) 1:12
Solution :
Ratio of their radius is 1:2.
Let r and 2r be their radius.
Ratio of their heights is 1:3 .
Let h and 3h be their respective heights.
Therefore, their respective volumes
(1/3) (pi) (r2) h ....(1)
(1/3) (pi) (2r)2 (3h) .....(2)
Divide 1 by 2, we have
(1/3) (pi) (r2) h / (1/3) (pi) (2r)2 (3h)
= 1/12
Hence the required ratio is 1:12.
Question 10
Find the X value from 0.35% of X = sqrt(8.41) + 3.62 - .78% of 500.
a) 748 b) 746 c) 750 d) 741
Answer : a) 748
Solution :
Given expression is 0.35% of X = sqrt(8.41) + 3.62 - .78% of 500
0.35X/100 = sqrt(8.41) + 3.62 - .78 x 500/100
35X/100 x 100 = 2.9 + 3.62 - 78 x 500/100 x 100
35X/10000 = 6.52 - 78 x 500/10000
35X/10000 = [(6.52 x 10000) - 78x500]/10000
35X = (6.52 x 10000) - 78 x 500
35X = 65200 - 39000 = 26200
X = 26200/35 = 5240/7 = 748 4/7
Hence the approximate X value is 748.
Question 11
If 85% - X = 81 3/7 % - 72 8/11 % then X is equal to
a) 0.52 b) 0. 98 c) 0.76 d) 0.65
Answer : c) 0.76
Solution :
Given expression is 85% - X = 81 3/7 % - 72 8/11 %
85% - 81 3/7 % + 72 8/11 % = X
85/100 - 570/7x100 + 800/11x100 = X
85 - 570/7 + 800/11 = 100X
77 x 85 - 570 x 11 + 800 x 7 = 100X x 77
6545 - 6270 + 5600 = 7700X
5875 = 7700X
X = 0.76 (approximately)
Question 12
The value of X in the expression .15% of X% of 3600% = 30% of 9.32 + 30 is:
a) 60733 b) 61732 c) 61329 d) 60512
Answer : a) 60733
Solution :
Given that, .15% of X% of 3600% = 30% of 9.32 + 30
.15/100 x X/100 x 3600/100 = 30/100 x 9.32 + 30
15X/1000000 x 36 = 932x30/10000 + 30
15X/1000000 x 36 = 932x3000/1000000 + 30000000/1000000
36 x 15X = 932 x 3000 + 30000000
540X = 2796000 + 30000000
X = 32796000/540 = 60733 (approximately)
Question 13
If 48.4% of 9500 = 10100 - 5% of 10100 - X then X value is:
a) 5001 b) 4997 c) 5109 d) 4907
Answer : b) 4997
Solution :
Given that, 48.4% of 9500 = 10100 - 5% of 10100 - X
X = 10100 - 5% of 10100 - 48.4% of 9500
X = 10100 - 5x10100/100 - 48.4x9500/100
X = 10100 - 5x101 - 48.4x95
X = 10100 - 505 - 4598 = 4997.
Question 14
If the radius of a cone is multiplied by 1/3 and height of the cone is tripled then the volume of new cone:
a) increases by one fourth b) increases by one third c) remains the same d) decreases thrice
Answer : b) increases by one third
Solution :
Let h and r be the height and radius of the cone
Then 3h and r/3 are the height and radius of new cone respectively.
We know that, the volume of a right circular cone of height h and radius r is 1/3 (pi)(r2)h unit3.
Now, the volume of the cone = 1/3 (pi) (r2)h.
Volume of new cone = 1/3 (pi) (r / 3)2 (3h) = 1/9 (pi) (r2) h
= 1/3 (1/3 (pi) (r2)h) = 1/3 x volume of of the cone.
Hence the answer is option b.
Question 15
If 3:2 is the ratio of radius of two right circular cones and 1:1 is the ratio of their volumes. Then what will
be the ratio of their heights ?
a) 1:3 b) 2:3 c) 7:2 d) 4:9
Answer : d) 4:9
Solution:
Ratio of radius = 3:2
Let their radius be 3X and 2X.
And 1:1 is the ratio of their volume which means they have equal volume.
Let h and H be their respective heights.
Then, (1/3) (pi) (3X)2 (h) = (1/3) (pi) (2X)2 (H)
9X2 (h) = 4X2 (H)
h / H = 4 / 9.
Hence required ratio is 4:9.