Question

1. The sum of a two digit number and the
number obtained by revosing the modern
of its digits is 165. If the digits differ
by 3 Find the number.
​

Answer 1

Let the unit place digit is X

& Ten's place digit is Y

According to first condition ;

(10X+Y)+(10Y+X) = 165

11X + 11Y = 165 ...............{1}

According to second condition ;

X - Y = 3 .....................{2}

Multiply second equation by 11

11X + 11 Y = 165

+

11X - 11Y = 33

___________________

22X = 198

X = 198 ÷ 22

X = 9

Put X = 9 in equation { 2 }

X - Y = 3

9 - Y = 3

- Y = 3 - 9

Y = 6

HENCE ANSWER IS : { 9 , 6 }

Hence the number is : 10X + Y : 10(9)+6. : 96

HOPE THIS HELPS YOU

Answer 2

let the numbers be x and y

The sum of a two digit number and the

number obtained by revosing the modern

of its digits = 165

reversing the digits = 10y + x

10x + y + 10y + x = 165

11x + 11y = 165

11(x + y ) = 165

x + y = 165/11

x + y = 15 ------(1)

the difference between the digits = 3

According to the problem,

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

Number = 10x + y

Add eq - (1) & (2)

x + y + x - y = 15 + 3

2x = 18

x = 18/2

x = 9

Substitute x in eq - (1)

(9) - y = 3

9 - 3 = y

y = 6

Number = 10x + y = 10(9) + 6 = 96

Therefore, the number is 96