Q .)A number is as much greater than 36 as is less than 86.
Find the number.

(a) 60
(b) 88
(c) 61
(d) 87

(ans:-) (C).
Let the number be x. Then, x - 36 = 86 - x => 2x = 86 + 36 = 122 => x = 61.
Hence, the required number is 61.

Q .)Find a number such that when 15 is subtracted from 7 times the number, the
Result is 10 more than twice the number ?

(a) 5
(b) 8
(c) 6
(d) 7

(ans:-)(A)
Let the number be x. Then, 7x - 15 = 2x + 10 => 5x = 25 =>x = 5.
Hence, the required number is 5.

Q .)The sum of a rational number and its reciprocal is 13/6.
Find the number ?

(a) 2/3
(b) 3/2
(c) (a) & (b) both
(d) none of these.

(ans:-) (C)
Let the number be x.
Then, x + (1/x) = 13/6 => (x2 + 1)/x = 13/6 => 6x^{2}-13x + 6 = 0
=> 6x^{2}-9x-4x + 6 = 0 => (3x-2) (2x-3) = 0
=> x = 2/3 or x = 3/2
Hence the required number is 2/3 or 3/2.

Q .)The sum of two numbers is 184. If one-third of the one exceeds one-seventh
of the other by 8, find the smaller number ?

(a) 78
(b) 74
(c) 73
(d) 72

(ans:-) (D)
Let the numbers be x and (184 - x). Then,
(X/3) - ((184-x)/7) = 8 => 7x-3(184-x) = 168 => 10x = 720 => x = 72.
So, the numbers are 72 and 112. Hence, smaller number = 72.

Q .)The difference of two numbers is 11
and one-fifth of their sum is 9. Find the numbers.?

(a) 28 & 18
(b) 18 & 27
(c) 28 & 17
(d) 16 & 17

(ans:-) (C)
Let the number be x and y. Then,
x-y = 11 ----(i) and 1/5 (x + y) = 9 => x + y = 45 ----(ii)
Adding (i) and (ii), we get: 2x = 56 or x = 28. Putting x = 28 in (i), we get: y = 17.
Hence, the numbers are 28 and 17.