Problems on Numbers for Exam
Q81. A two digit number is three times the sum of its digits. If 27 is added to the number, its digits are interchanged. The sum of the digits of the number is
(a) 5.4
(b) 3.7
(c) 2.9
(d) 7.3
Answer: (a) 5.4
Let the unit digit number be x and
the ten's digit number be y
∴ Number = 10y + x
A/Q 10y + x = 3 (y + x)
⇒ 10y + x = 3y + 3x
⇒ 7y - 2x = 0 --------> (1)
And 10y + x + 27 = 10x + y
⇒ 9y - 9x = -27
⇒ y - x = -3
⇒ x - y = 3
⇒ 2x - 2y = 6 ------> (2)
(1) + (2) ⇒ 5y = 6
⇒ y = 6/5
(2) ⇒ 2x = 6 + 2 X (6/5)
⇒ 2x = 6 + (12/5)
⇒ 2x = 42/5
⇒ x = 42/10
| ∴ x + y = | 42 | + | 6 |
| 10 | 5 |
| = | 42 + 12 |
| 10 |
| = | 54 |
| 10 |
= 5.4
Q82. A two digit number is 7 times the sum of its digits. The number formed by reversing its digits is 27 less than the original number. What is the number ?
(a) 41
(b) 45
(c) 54
(d) 63
Answer: (d) 63
Let, unit digit = x
ten's digit = y
∴ Number = 10y + x
A/Q 10y + x = 7 (x + y)
⇒ 10y + x = 7x + 7y
⇒ 3y - 6x = 0
⇒ 2x - y = 0 ------> (1)
And 10x + y + 27 = 10y + x
⇒ 9x - 9y = -27
⇒ x - y = - 3
⇒ y - x = 3 --------> (2)
(1) + (2) ⇒ x = 3
(2) ⇒ y = 3 + 3 = 6
∴ Number = 10 X 6 + 3 = 63
Q83. The difference between two digit number and the number obtained by interchanging the positions of its digits is 36. The digit at unit place is one-third of the digit at ten's place in the original number. What is the original number ?
(a) 49
(b) 56
(c) 62
(d) 71
Answer: (c) 62
Let, the tens digits be x
∴ the unit digits be x/3
| A/Q (10x + | x | ) - ( | 10x | + x) = 36 |
| 3 | 3 |
⇒ 9x - 3x = 36
⇒ x = 6
∴ Original number = 62
Q84. The sum of two number is 64. If three times of one number is equal to five times of the other, find the numbers
(a) 30 and 20
(b) 35 and 25
(c) 40 and 24
(d) 55 and 32
Answer: (c) 40 and 24
Let, one number be x
∴ Another number is (64 - x)
A/Q 3x = 5 (64 - x)
⇒ 3x = 320 - 5x
⇒ 8x = 320
⇒ x = 40
∴ Numbers are 40 and 24
Q85. The sum of three consecutive multiples of 2 is 78. What is the smallest of these numbers ?
(a) 21
(b) 24
(c) 27
(d) 33
Answer: (b) 24
Let numbers are 2x, 2x+2, 2x+4
A/Q 2x + 2x + 2 + 2x + 4 = 78
⇒ 6x + 6 = 78
⇒ 6x = 72
⇒ x = 12
∴ Smallest number = 2 X 12 = 24
Q86. The sum of three consecutive multiples of 3 is 99. What is the largest of these numbers ?
(a) 20
(b) 25
(c) 28
(d) 36
Answer: (d) 36
Let numbers are 3x, 3x+3, 3x+6
A/Q 3x + 3x + 3 + 3x + 6 = 99
⇒ 9x + 9 = 99
⇒ 9x = 90
⇒ x = 10
∴ The largest number = 3 X 10 + 6 = 36
Q87. If the difference between 3/5 th and 3/7 th of a number is 54, then the number would be
(a) 231
(b) 252
(c) 297
(d) 315
Answer: (d) 315
Let the number be x
A/Q x X (3/5) - x X (3/7) = 54
⇒ (3x/5) - (3x/7) = 54
⇒ 6x/35 = 54
⇒ x = 315
Q88. 15% of a number is 135. What is the 30% of the number ?
(a) 215
(b) 270
(c) 311
(d) 342
Answer: (b) 270
Let the number be x
A/Q x X 15% = 135
⇒ x X (15/100) = 135
⇒ x = 900
∴ 30% of 900 = (30/100) X 900 = 270
Q89. The product of two consecutive even numbers is 440. The numbers are
(a) 20 and 22
(b) 20 and 25
(c) 23 and 28
(d) 27 and 32
Answer: (a) 20 and 22
Let the numbers are x, x+2
A/Q x(x+2) = 440
⇒ x2 + 2x - 440 = 0
⇒ x2 + 22x - 20x - 440 =0
⇒ x(x+22) - 20(x+22) = 0
⇒ (x+22) (x-20) = 0
∴ x + 22 = 0 or x - 20 = 0
∴ x = -22 or x = 20
∴ The number are 20, 22
Q90. 2/5 of a number is 12 less than the original number. The number is
(a) 12
(b) 17
(c) 20
(d) 24
Answer: (c) 20
Let, the number be x
A/Q x X (2/5) + 12 = x
⇒ (2x/5) + 12 = x
| ⇒ | 2x + 60 | = x |
| 5 |
⇒ 2x + 60 = 5x
⇒ 3x = 60
⇒ x = 20
Practice Test Exam