Question

4. The sum of a two digit numbers and number formed by interchanging the digit is 132. If 12 is added to number, the new number becomes 5 times the sum of the digits. Find number.

Answer 1

ANSWER:

• Original number = 48

GIVEN:

• The sum of a two digit numbers and number formed by interchanging the digit is 132.
• If 12 is added to number, the new number becomes 5 times the sum of the digits.

TO FIND:

• Original number

SOLUTION:

• Let the digit at tens place = 'x'.
• Let the digit at once place = 'y'

Original Number = 10x+y

Reversed number = 10y+x

Now according to the question:

CASE 1

=> 10x+y +10y+x = 132

=> 11x + 11y = 132

=> 11(x+y) = 132

=> (x+y) = 132/11

=> (x+y) = 12. .......(i)

Multiplying both sides by 4 we get;

=> 4x + 4y = 48. ......(ii)

CASE 2

=>10x +y +12 = 5(x+y)

=> 10x+y +12 = 5x+5y

=>10x-5x +y- 5y = (-12)

=> 5x +4y = (-12). ......(iii)

Adding eq (ii) and (iii) we get;

=> 5x+4x +4y -4y = 48-12

=> 9x = 36

=> x = 4

Now; putting x = 4 in eq (i) we get;

=> 4+y = 12

=> y = 8

Original number = 10*4+8

=48