Problems on Numbers for Exam
Q101. 3/4 th of 2/3 rd of a number is 782. What is 3/5 th of 1/4 th of the same number ?
(a) 112.3
(b) 165.3
(c) 214.7
(d) 234.6
Answer: (d) 234.6
Let the number be x
A/Q 3/4 X 2/3 X x = 782
⇒ x = 782 X (12/6)
⇒ x = 1564
Now 3/5 X 1/4 X 1564
= (3 X 1564)/(5 X 4) = 234.6
Q102. If the difference between the reciprocal of a positive proper fraction and the fraction itself be 9/20 , then the fraction is
(a) 4/5
(b) 4/7
(c) 5/7
(d) 5/9
Answer: (a) 4/5
Let the fraction be x
A/Q 1/x - x = 9/20
⇒ (1 - x2)/x = 9/20
⇒ 20 - 20x2 = 9x
⇒ 20x2 + 9x - 20 = 0
⇒ 20x2 + 25x - 16x - 20 = 0
⇒ 5x(4x + 5) - 4(4x + 5) = 0
⇒ (4x + 5) (5x - 4) = 0
∴ 4x + 5 = 0 or 5x - 4 = 0
⇒ x = - 5/4 ⇒ x = 4/5
∴ The fraction = 4/5
Q103. Summation of a whole number and its reciprocal is 50/7. What is the number ?
(a) 5
(b) 7
(c) 8
(d) 10
Answer: (b) 7
Let the fraction be x
| A/Q x + | 1 | = | 50 |
| x | 7 |
| ⇒ | x2 + 1 | = | 50 |
| x | 7 |
⇒ 7x2 + 7 = 50x
⇒ 7x2 - 50x + 7 = 0
⇒ 7x2 - 49x - x + 7 = 0
⇒ 7x(x - 7) - 1 (x - 7) = 0
⇒ (x - 7) (7x - 1) = 0
∴ x = 7 7x - 1 = 0 ⇒ x = 1/7
∴ The number is 7
Practice Test Exam