Question

The sum of the digits of a two digit number is 13.The number obtained by interchanging its digits exceeds the given number by 9.Find the number.

(Answer:67)

Answer 1

Dear student,

Let x be the tens place digit and y be the unit place digit of a two digit number.

then, original number is =10x+y

from first condition

x+y=13 ----------(1)

from second condition ie, The number obtained by interchanging
its digits exceeds the given number by 9

So we can say,
10y+x=10x+y+9

=> x-10x+10y-y=9
=> -9x+9y=9

dividing by 9
=> -x+y=1 ----------(2)

adding equation (1 )and( 2)

we will get

2y=14
y=14÷2
y=7

putting y=7 in equation ----(1)

x+y=13
will be

x+7=13
x=13-7
x=6

original number=10x+y=10×6+7

=60+7=67

Hope you understood
Enjoy learning!!
Regards