Question

A two digit number is 4 more than the sum of its digits. if 18 is added to the number , the digits are reversed . find number​

Answer 1

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Let the two-digit number be xy.

$T | O\\x \: | y$

Do you know the standard form of number? Here's an example so that you can recollect:

1534 = 1000×1+500×1+30×1+4

If we expand the number xy we will get:

⇒10x+y

Now, the question states:

A two digit number is 4 more than the sum of its digits.

The number would be 10x+y (aasumed above) and the sum of the digits woul be x+y. Thus, we can form this equation:

10x + y = 4 (x + y)  

10x + y = 4x + 4y

6x = 3y

y = 2x

y - 2x = 0-----------(1)

Now, consider the second part of the question.

If 18 is added to the number , the digits are reversed. So, we know that the number is xy. If it is reversed, it would be yx.

Standard form of xy is 10x+y, standard form of yx is 10y+x.

Equation:

10x + y + 18 = 10y + x

9y - 9x = 18

Take 9 common.

9 (y - x) = 18

y - x = 18/9

y - x = 2 ----------(2)

Subtract 1 and 2.

$y - 2x = 0 \\y - 1x = 2 (-) \\ ------\\x=2$

Substitute the value of x in any equation:

y = 2x.

y = 2×2

y = 4.

We know that the number we assumed was 10x+y. Substitute the values of x and y.

⇒10×2+4

⇒24.

THE NUMBER IS 24.

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