# Aptitude Problems on Numbers Test Paper 2

16) The product of two numbers is 300, and the sum of their squares is 625. What are the numbers?

1. 1025
2. 1125
3. 1225
4. 1325

Explanation:

Let the numbers be x and y.
As per the question:

xy = 300
x2 + y2 = 625

So, (x+y)2 = x2 + y2 + 2xy
= 625 + 2 * 300
= 625 + 600
= 1225

17) The difference between a two-digit number and the number obtained by interchanging the position of the digits is 45. What is the difference between digits of that number?

1. 6
2. 5
3. 7

Explanation:

Let the number be = xy
so the ten's digit = x
Unit's digit = y
So, the number is = 10x +y
Number obtained by interchanging the digits = 10y + x
According to the question:
(10x + y) - (10y + x) = 45
10x + y - 10y - x = 45
9x - 9y = 45
9(x - y) = 45
X - Y = 5
∴The difference between the digits of the numbers: (x - y) = 5

18) When the numerator of a certain fraction is increased by 1 and the denominator by 2, it changes to ; but when the numerator is increased by 5 and the denominator by 1, the value of the fraction changes to . What is the original fraction? Explanation:

Let the fraction be .

As per the question: 3x + 3 = 2y + 4
3x - 2y = 1 ..... (i)

As per the question: 4x + 20 = 5y + 5
4x - 5y = - 15 ..... (2)

Solving equation ((1) and (2), we get:

-x + 3y = 16 So, -x = 16 - 3y or x = -16 + 3y

Put the value of x in equation (i)

3 (-16 + 3y) - 2y = 1
- 48 + 9y - 2y = 1
-48 + 7y = 1
7y = 1 + 48
7y = 49
y = 7

Now, put the value of Y in equation (i)

3x - 2 * 7 = 1
3x = 1 + 14
3x =15
x = 5
X = 5, y = 7
So, the required fraction is 19) The difference between a two-digit number and the number obtained by changing the positions of its digits is 36. What is the difference between the two digits of that number?

1. 3
2. 4
3. 9
4. Cannot be determined.
5. None of these.

Explanation:

Let the number be = xy

So, the ten's digit is x and the unit's digit is y.

As per the question:

(10x + y) - (10y + x) = 36
10x + y - 10y - x = 36
9x - 9y = 36
9(x - y) = 36
x - y = 4

20) A two-digit number is such that the product of the digits is 8. When 18 is added to the number, then the digits are reversed. Find the number.

1. 18
2. 24
3. 42
4. 81

Explanation:

Let the ten's and unit digit be x and , respectively. 10x2 + 8 + 18x = 80 + x2
9x2 + 18x - 72 = 0
x2 + 2x - 8 = 0
(x + 4)(x - 2) = 0
x = 2.

Ten's place= 2
Unit's place = 8/2 = 4
So, the number is 24.

Aptitude Problems on Numbers Test Paper 1
Aptitude Problems on Numbers Test Paper 2
Aptitude Problems on Numbers Test Paper 3
Problems on Numbers Concepts   