Question

a number consisting of two digits is 7 times the sum of its digits when 27 is subtracted from the number the digits are reversed find the number

Answer 1

Heya !!

Here's your answer.. ⬇⬇
________________________________

Let the ten's place = x
unit place = y

original no. = 10x + y

➡ Given that a number consisting of two digits is 7 times the sum of its digit.

10x + y = 7 ( x + y )
10x + y = 7x + 7y
10x - 7x + y - 7y = 0
3x - 6y = 0
3( x - 2y ) = 0
x - 2y = 0 ---–(1)

➡ when 27 is subtracted from the number the digits are reversed.

Reversed no. = 10y + x

10x + y - 27 = 10y + x
10x - x + y - 10y = 27
9x - 9y = 27
9 ( x - y ) = 27
x - y = 3 ------(2)

Subtract eq. ( 2) from eq. (1)

x - 2y = 0
-x + y = -3
-----------------
- y = - 3
y = 3

Put value of ( y ) in eq. ( 1)

x - 2y = 0
x - 2( 3 ) = 0
x - 6 = 0
x = 6

original no. = 10x + y
= 10( 6 ) + 3
= 60 + 3
= 63

_______________________________
Hope it helps..

Thanks :))