A two digit number is such that the sum of the ones and the tens digits is tens. If the digits are reversed, the new number formed exceeds the originals numbers by 54.Find the number.

Explanation:

Let the no in the ones place be x

And the no in the tens place be 10 - x

Original no = 10 ( 10 - x ) + x

= 100 - 10x + x

= 100 - 9x

Reversed no = 10 - x + 10 ( x )

= 10 - x + 10 x

10 + 9x

According to the question,

the new number formed exceeds the originals numbers by 54.

10 + 9x = 100 - 9x + 54

10 + 9x = 154 - 9x

By transposing,

9x + 9x = 154 - 10

18 x = 144

x = 144 / 18

x = 8

∴ Digit in ones place = x = 8

Digit in tens place = 10 - x = 10 - 8 = 2

So the number = 28

( You can also recheck it by adding the ones and tens digit

8 + 2 = 10

In the question, the sum of ones and tens digit in ten )

Hope this helps

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