Question

sum of the digits of a two digit number is 12 when we interchange the digits, it is great then 30 what is the two digit number? ​

Answer 1

Step-by-step explanation:

*Given:Sum of the digits of a two digit number is 12 when we interchange the digits, it is great then 36.

To find: what is the two digit 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;

$x + y = 12...eq1$

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

$10y + x = 10x + y + 36 \\ \\ 9x - 9y = 36 \\ \\ or \\ \\ x - y = - 4 \: \: ...eq2$

Add both equations

$x + y = 12 \\ x - y = - 4 \\ - - - - - - - \\ 2x =8 \\ \\ \red{x = 4}$

put the value of x in eq1

$x + y = 12 \\ \\ 4 + y = 12 \\ \\ \red{y =8 }$

The number is 48.

Final answer:

The two digit number is 48.

Verification:

$4+8=12 \\ \\ 48 + 36 = 84$

Hope it helps you.

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