Question

The sum of digits of a two digit number is 7. A number obtained after interchanging the digits is 27 more than the original number. Find the original number.​

Answer 1

Step-by-step explanation:

Given:The sum of digits of a two digit number is 7. A number obtained after interchanging the digits is 27 more than the original number.

To find: Find the original number.

Solution:

Let the number is xy.

It's unit digit is y and tenth digit is x.

ATQ

The sum of digits of a two digit number is 7;

$x + y = 7...eq1$

A number obtained after interchanging the digits is 27 more than the original number

Two digit number can be expressed in expanded form as 10x+y

According to condition

$10y + x = 10x + y + 27 \\ \\ 9x - 9y = -27 \\ \\ or \\ \\ x - y = - 3 \: \: ...eq2$

Add both equations

$x + y = 7 \\ x - y = - 3 \\ - - - - - - - \\ 2x = 4 \\ \\ \red{x = 2}$

put the value of x in eq1

$x + y = 7 \\ \\ 2 + y = 7 \\ \\ \red{y = 5 }$

The number is 25.

Final answer:

The two digit number is 25.

Verification:

$5 + 2 = 7 \\ \\ 25 + 27 = 52$

Hope it helps you.

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