- The difference of the digits of a 2-digit number is 3. If the digits

1.	- The difference of the digits of a 2-digit number is 3. If the digits are interchanged and thenew number is added to the original number, the result is 77. Find the original number.
Answer» 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*

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

Answer»

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

so,

original number = 52 or 25

hope it helps