Problems on Numbers for Exam
Q61. 60% of a number is 304 more than 40% of the same number. What is 25% of that number ?
(a) 349
(b) 365
(c) 380
(d) 410
Answer: (c) 380
Let the number be x
A/Q, x X 60% = x X 40% + 304
⇒ x X (60/100) = x X (40/100) + 304
| ⇒ x X | 3 | - x X | 2 | = 304 |
| 5 | 5 |
| ⇒ | 3x - 2x | = 304 |
| 5 |
⇒ x = 304 X 5 = 1520
Now 25% of 1520 = (25/100) X 1520 = 380
Q62. A number is 28 more than its 2/7th. The number is
(a) 168/7
(b) 147/4
(c) 196/5
(d) 181/6
Answer: (c) 196/5
Let the number be x
A/Q, x = x X (2/7) + 28
⇒ x = (2x/7) + 28
⇒ x = (2x + 196) / 7
⇒ 7x - 2x = 196
⇒ 5x = 196
⇒ x = 196/5
Q63. If 20% of 13/12 of a certain number is 520, then what is 60% of that number ?
(a) 1104
(b) 1132
(c) 1256
(d) 1440
Answer: (d) 1440
Let the number be x
A/Q, x X 20% of 13/12 = 520
⇒ x X (20/100) X (13/12) = 520
⇒ (13x/60) = 520
⇒ x = (520 X 60) / 13 = 2400
Now 60% of 2400 = (60/100) X 2400 = 1440
Q64. The product of two positive numbers is 8000 and their quotient is 9/5. Their difference is
(a) 47.23
(b) 53.34
(c) 58.66
(d) 61.47
Answer: (b) 53.34
Let the numbers be a and b
A/Q, a X b = 8000 -----> (1)
and a/b = 9/5 ------> (2)
(1) X (2) ⇒ ab X (a/b) = 8000 X (9/5)
a2 = 14400
a2 = (120)2
⇒ a = 120
(1)⇒ b = 8000 / 120 = 66.66
Now a - b = 120 - 66.66 = 53.34
Q65. The denominator of a fraction is 1 more than its numerator. If 1 is deducted from both the numerator and denominator, the fraction becomes ½ . The fraction is
(a) 2/3
(b) 2/5
(c) 3/5
(d) 4/7
Answer: (a) 2/3
Let the numerator be x
∴ The denominator = x + 1
| ∴ Fraction = | x |
| x + 1 |
| A/Q | x - 1 | = | 1 |
| (x + 1) - 1 | 2 |
| ⇒ | x - 1 | = | 1 |
| x | 2 |
⇒ 2x -2 = x
⇒ x = 2
∴ Fraction = 2/(2+1) = 2/3
Q66. The difference between a number and its 3/5 th is 260 more than 3/5 th of the number. The number is
(a) - 575
(b) - 900
(c) - 1150
(d) - 1300
Answer: (d) - 1300
Let the number be x
| A/Q, x - x X | 3 | = x X | 3 | + 260 |
| 5 | 5 |
| ⇒ x - | 3x | = | 3x | + 260 |
| 5 | 5 |
| ⇒ x - | 3x | - | 3x | = 260 |
| 5 | 5 |
| ⇒ | 5x - 3x - 3x | = 260 |
| 5 |
| ⇒ | -x | = 260 |
| 5 |
⇒ x = -260 X 5 = -1300
Q67. If one number is 3/5 rd of other number and their sum is 80, then the first number is
(a) 25
(b) 30
(c) 32
(d) 38
Answer: (b) 30
Let the first number be x
∴ the other number be 80 - x
| A/Q, x = | 3 | X (80 - x) |
| 5 |
⇒ 5x = 240 - 3x
⇒ 8x = 240
⇒ x = 30
Q68. The sum of the square of two positive integers is 100 and the difference of their square is 28. The sum of the numbers is
(a) 14
(b) 21
(c) 26
(d) 29
Answer: (a) 14
Let the integers be x and y
A/Q, x2 + y2 = 100 -------> (1)
x2 - y2 = 28 -------> (2)
(1) + (2) ⇒ 2x2 = 128
⇒ x2 = 64
⇒ x = 8
(1)⇒ y2 = 100 - x2 = 100 - 64 = 36
∴ y = 6
∴ x + y = 8 + 6 = 14
Q69. If the sum and difference of two numbers are 30 and 10 respectively then the difference of their squares is
(a) 150
(b) 200
(c) 300
(d) 400
Answer: (c) 300
Let the numbers be x and y
A/Q, x + y = 30 -------> (1)
x - y = 280 -------> (2)
(1) + (2) ⇒ 2x = 40
⇒ x = 20
(1)⇒ y = 30 - 20 = 10
Now x2 - y2 = 202 - 102 = 400 - 100 = 300
Q70. If the sum of the two numbers is 20 and the sum of their square is 300, then the product of the number is
(a) 30
(b) 50
(c) 70
(d) 90
Answer: (b) 50
Let the numbers be x and y
A/Q, x + y = 320 -------> (1)
and x2 + y2 = 300 -------> (2)
(1) ⇒ (x + y)2 = 202
⇒ x2 + y2 + 2xy = 400
⇒ 300 + 2xy = 400
⇒ 2xy = 100
⇒ xy = 50
Practice Test Exam