Question

The sum of the digits of a two digit number is 15. If the number formed by reversing the digits is less than the original number by 27. Find the original number. [4]​

Answer 1

$\tt\huge \: \underline {To Find }: \:$

• Find the original number.

$\tt\huge \: \underline {Given }: \:$

• The sum of the digits of a two digit number is 15.
• If the number formed by reversing the digits is less than the original number by 27.

$\tt\huge \: \underline { Solution }: \:$

Let the unit place be " x "

Then ten's places be " 15 - x "

Original number = 10 ( 15 - x ) + x

$\tt\implies \: 150 - 10x + x \:$

$\tt\implies \: 150 - 9x \:$

Reversing digit we get,

$\tt\implies \: New \: \: number \: \: formed = 10x + (15 - x)\:$

$\tt\implies \: 10x + 15 - x \:$

$\tt\implies \: 9x + 15 \:$

By reversing the digits is less than the original number by 27.

Original number - new number = 27

$\tt\implies \: ( 150 - 9x ) - ( 9x + 15 ) = 27 \:$

$\tt\implies \: 150 - 9x - 9x - 15 = 27 \:$

$\tt\implies \: 135 - 18x = 27 \:$

$\tt\implies \: -18x = 27 - 135 \:$

x = -108/-18

$\tt\implies \: x = 6 \:$

So,

Original number = 10 ( 15 - x ) + x

10( 15 - 6 ) + 6

10(9) + 6

90 + 6

96

Answer 2

{ To Find }

Find the original number.

{Given }

The sum of the digits of a two digit number is 15.

If the number formed by reversing the digits is less than the original number by 27.

{ Solution }

Let the unit place be " x "

Then ten's places be " 15 - x "

Original number = 10 ( 15 - x ) + x

⟹150−10x+x

⟹150 - 9x

Reversing digit we get,

⟹New number formed=10x + (15−x)

⟹10 x + 15 − x

⟹9 x + 15

By reversing the digits is less than the original number by 27.

Original number - new number = 27

⟹(150 − 9x)−(9x + 15)=27

15)=27⟹150 − 9x−9x−15=27

9x−9x−15=27⟹135−18x=27

9x−9x−15=27⟹135−18x=27⟹−18x=27−135

9x−9x−15=27⟹135−18x=27⟹−18x=27−135x = -108

x = 6

So ,

Original number = 10 ( 15 - x ) + x

• 10( 15 - 6 ) + 6

• 10(9) + 6

• 90 + 6

• 96