Question

- The difference of the digits of a 2-digit number is 3. If the digits are interchanged and the
new number is added to the original number, the result is 77. Find the original number.​

Answer 1

Answer:

52 or 25

Step-by-step explanation:

let the digits of two digit number be x and y

so,

number will be

10x + y

given that

,The difference of the digits = 3

so,

x - y = 3 .....(1)

and

also given that

If the digits are interchanged

(means 10x + y to 10y + x)

then

new number is added to the original number, the result is 77

original number is 10x + y

number formed by interchanging of digits

= 10y + x

ATQ,

10x + y + 10y + x = 77

11x + 11y = 77

x + y = 77/11

x + y = 7 .....(2)

now from eqn (1) and (2)

by adding both

x - y + x + y = 3 + 7

2x = 10

x = 10/2

x = 5

putting the value of x on (1)

x - y = 3

5 - y = 3

-y = 3 - 5

-y = -2

y = 2

x = 5

original number = 10x + y

= 10(5) + 2

50 + 2

52

so,

original number = 52 or 25

hope it helps