Question

The sum of 2 digit no and the number formed by interchange the digit is 132.if 12 is added to the number the new number become 5 times the sum of digit find number​

Answer 1

let the two digit no. be 10x + y

and the no. when reversed be 10y + x

according to the question :

10x + y + 10y + x = 132

11x + 11y = 132

taking 11 common

11(x + y ) = 132

x + y = 12 ----------- 1)

lets do the second part

Now,

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

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

5x + 12 = 4y

4y - 5x = 12 ------ 2)

substituting y = 12 - x in equation 2)

4( 12 - x ) - 5x = 12

48 - 4x - 5x = 12

48 - 12 = 9x

36 = 9x

x = 4

x + y = 12

4 + y = 12

y = 8

so the no. is 48

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Answer 2

QUESTION -

The sum of 2 digit no and the number formed by interchange the digit is 132.if 12 is added to the number the new number become 5 times the sum of digit find number

ANSWER -

let the two digit number be xy => value is 10x+y

if the digits are reversed, value is 10y+x

given

10x+y+10y+x=132

11x +11y = 132

x+y=12..............(1)

if 12 is added value is 10x+y+12

given

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

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

10x+y-5x-5y= -12

5x-4y = -12..................(2), solve (1) and (2)

(1)x4 =>

4x+4y=48

5x-4y = -12 add

9x = 36 => x = 4

(1)=> 4+y=12 => y=8

the number is 48