Problems on Numbers for Exam
Q91. 2/3 of a certain number is 12. Half of the number be
(a) 9
(b) 12
(c) 15
(d) 17
Answer: (a) 9
Let the number be x
A/Q | 2 | X x = 12 |
3 |
⇒ | 2x | = 12 |
3 |
⇒ x = 18
∴ Required number = 18/2 = 9
Q92. The difference of two numbers is 8 and 1/8 th of their sum is 35. The numbers are
(a) 115, 92
(b) 120, 112
(c) 132, 128
(d) 144, 136
Answer: (d) 144, 136
Let one number be x
∴ another number is x - 8
A/Q {x + (x - 8)} X (1/8) = 35
⇒ x + x - 8 = 35 X 8
⇒ 2x = 280 + 8
⇒ x = 144
∴ The numbers are 144, (144 - 8) = i.e 144, 136
Q93. Of the three numbers, the sum of first two is 35, the sum of the second and the third is 45 and the sum of the third and the first is 80. The first number is
(a) 31
(b) 35
(c) 42
(d) 56
Answer: (b) 35
Let, the numbers be x, y, z
A/Q x + y = 35 -----> (1)
y + z = 45 -----> (2)
z + x = 80 ------> (3)
(1) + (2) + (3) ⇒ 2x + 2y + 2z = 35 + 45 + 80
⇒ 2 (x + y + z) = 160
⇒ x + y + z = 80
⇒ 35 + z = 80
⇒ z = 45
⇒ x = 80 - 45 = 35
∴ First number is 35
Q94. 50 divided into two parts such that the sum of their reciprocals is 1/12. These parts are
(a) 30, 20
(b) 35, 40
(c) 40, 42
(d) 50, 55
Answer: (a) 30, 20
Lets the parts be x and (50 - x)
A/Q | 1 | + | 1 | = | 1 |
x | 50-x | 12 |
⇒ | 50 - x + x | = | 1 |
x (50 - x) | 12 |
⇒ 600 = 50x - x2
⇒ x2 - 50x + 600 = 0
⇒ x2 - 30x - 20x + 600 = 0
⇒ x(x - 30) - 20(x - 30) = 0
⇒ (x - 30) (x - 20) = 0
∴ x - 30 = 0 or x - 20 = 0
⇒ x = 30 x = 20
∴ Parts are 30, 20
Q95. A number exceeds 10% of itself by 27. The number is
(a) 20
(b) 30
(c) 40
(d) 50
Answer: (b) 30
Let the number be x
A/Q x - x X 10% = 27
⇒ x - x X | 10 | = 27 |
100 |
⇒ | 10x - x | = 27 |
10 |
⇒ 9x = 270
⇒ x = 270/9
⇒ x = 30
Q96. Two-fifth of a number is more than one fourth of the number by 6. The number is
(a) 35
(b) 40
(c) 45
(d) 55
Answer: (b) 40
Let the number be x
A/Q x X | 2 | = x X | 1 | + 6 |
5 | 4 |
⇒ | 2x | = | x | + 6 |
5 | 4 |
⇒ | 2x | - | x | = 6 |
5 | 4 |
⇒ | 8x - 5x | = 6 |
20 |
⇒ | 3x | = 6 |
20 |
⇒ x = 40
Q97. What number must be added to the numerator and denominator of 2/5 to give 9/10 ?
(a) 18
(b) 21
(c) 25
(d) 32
Answer: (c) 25
Let the number be x
A/Q | 2 + x | = | 9 |
5 + x | 10 |
⇒ 20 + 10x = 45 + 9x
⇒ x = 45 - 20 = 25
Q98. A positive number added to its square gives 42. The number is
(a) 6
(b) 11
(c) 15
(d) 22
Answer: (a) 6
Let the number be x
A/Q x + x2 = 42
⇒ x2 + x - 42 = 0
⇒ x2 + 7x - 6x - 42 = 0
⇒ x (x + 7) - 6(x + 7) = 0
⇒ (x + 7) (x - 6) = 0
∴ x - 6 = 0
⇒ x = 6
Q99. If the sum of two numbers is 10 and the sum of their reciprocals is 5/12 , the numbers would be
(a) 2, 5
(b) 4, 6
(c) 5, 6
(d) 7, 5
Answer: (b) 4, 6
Let the numbers be x and (10 - x)
A/Q | 1 | + | 1 | = | 5 |
x | 10 - x | 12 |
⇒ | 10 - x + x | = | 5 |
x (10 - x) | 12 |
⇒ | 10 | = | 5 |
10x - x2 | 12 |
⇒ 120 = 50x - 5x2
⇒ 5x2 - 50x + 120 = 0
⇒ x2 - 10x + 24 = 0
⇒ x2 - 6x - 4x + 24 = 0
⇒ x(x - 6) - 4(x - 6) = 0
⇒ (x - 6) (x - 4) = 0
∴ x = 6 or x = 4
∴ Ans = 4, 6
Q100. If the numerator of a function is increased by 15% and the denominator of the fraction is increased by 30%, the resultant fraction is 5/18. What is the original fraction ?
(a) 32/115
(b) 46/107
(c) 65/207
(d) 69/219
Answer: (c) 65/207
Let the original fraction be x/y
A/Q | x + x X 15% | = | 5 |
y + y X 30% | 18 |
⇒ | x + 15x/100 | = | 5 |
y + 30y/100 | 18 |
⇒ | 115x | = | 5 |
130y | 18 |
⇒ | x | = | 5 X 130 |
y | 18 X 115 |
⇒ | x | = | 65 |
y | 207 |
Practice Test Exam