# Problems on Numbers Questions Quiz 1 PDF for CDS, CGL, CHSL, Railways

Directions: Study the following questions carefully and choose the right answer.
Important for :
1
A number is as much greater than 36 as is less than 86. Find the number :
» Explain it
C
Let the number be z. then, z – 36 = 86 – z

⇒  2z = 86 + 36 ⇒ 2z = 122.

⇒  z = 61.

Hence, the required number is 61.

Hence, option C is correct.

2
Find a number such that when 15 is subtracted from 7 times the number, the result is 10 more than twice the number.
» Explain it
A
Let, the number be z, Then, 7z – 15 = 2z + 10

⇒  5z = 25  ⇔ z = 5.

Hence, the required number is 5.

Hence, option A is correct.

3
The sum of the rational and its reciprocal is 13/6. Find the number.
» Explain it
C
Smart Approach:

We can easily solve this question by applying the 'Hit & Trial' approach.

The condition says that sum of the numbers and its reciprocal must be (13/6) and in

the 1st option, the sum of

 5 (the num) + 3 (its reciprocal) will give us 34 . 3 5 15

Option 'A'  hence gets eliminated.

the 2nd option, the sum of

 2 + 1 = 5 2 2

Option 'B' hence gets eliminated too.

the 3rd option, the sum of

 3 + 2 = 13 . 2 3 6

Option 'C' hence is the correct answer.
_________________________________________________________

Given expression:'
 Then, z + 1 = 13 z 6

 ⇒ z2 + 1 = 13 . z 6

⇒  6z2 – 13z + 6 = 0

⇒  6z2 – 9z – 4z + 6 = 0  ⇔  (3z – 2) (2z – 3) = 0

⇒  z = 2/3   or 3/2.

Hence, option C is correct.

4
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.
» Explain it
D
Let the number be z and (184 – z). then,

 ⇒ z – (184 – z ) = 8. 3 7

⇒  7z – 3(184 – z) = 168

⇒  10z = 720

⇒   z = 72.

Hence, option D is correct.

5
The difference of two numbers is 11 and one-fifth of their sum is 9. find the numbers.
» Explain it
B
Let the numbers be x and y. then,
x – y = 11           .....(1)      and,

 ⇒ 1 (x + y)  = 9 5

⇒  x + y = 45         ...(2)

Adding (1) and (2) we get :   2x = 56 or x = 28. putting x = 28 in (1), we get : y = 17.

Hence, the numbers are 28 and 17.

Hence, option B is correct.