Question

The sum of a two digits is 14.When the door gits of this number ate reversed, the new nimber is greater than the original no. by 36.Find the original no. ​

Answer 1

GIVEN:

• The sum of the digits of a two digit number is 14.
• Reversed Number is greater than the original number by 36.

TO FIND:

• What is the original number?

SOLUTION:

Let the digit at ten's place be 'x' and the digit at unit's place be 'y'

• NUMBER = 10x + y

CASE:- 1)

❐ The sum of the digits of a two digit number is 14.

➫ x + y = 14

➫ x = 14 –y...❶

CASE:- 2)

❐ Reversed Number is greater than the original number by 36.

➫ 10x + y = 10y + x + 36

➫ 10x + y –(10y + x) –36 = 0

➫ 10x + y –10y –x –36 = 0

➫ 9x –9y –36 = 0

➫ 9(x –y –4) = 0

➫ x –y –4 = 0...❷ 

Put the value of 'x' from equation 1) in equation 2)

➫ 14 –y –y –4 = 0

➫ 10 –2y = 0

➫ 10 = 2y

➫ $\sf{\cancel\dfrac{10}{2}}$ = y

❮ 5 = y ❯

Put the value of 'y' in equation 1)

➫ x = 14 –5

❮ x = 9 ❯

• NUMBER = 10x + y
• NUMBER = 10(9) + 5
• NUMBER = 90 + 5
• NUMBER = 95

❝ Hence, the number formed is 95 ❞

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Answer 2

$\sf{\underline{\boxed{\large{\blue{\mathsf{Correct\: Question}}}}}}$

• The sum of a two digits is 14.When the digits of this number are reversed, the new number is greater than the original no. by 36.Find the original no.

_______________________

$\sf{\underline{\boxed{\large{\blue{\mathsf{Solution}}}}}}$

$\sf{\bold{\green{\underline{\underline{Given}}}}}$

• Sum of 2 digits of 2 digit no = 14
• If the digits are reversed new no. is greater than the original no. by 36

_______________________

$\sf{\bold{\green{\underline{\underline{To\:Find}}}}}$

• The original number = ???

______________________

$\sf{\bold{\green{\underline{\underline{Solution}}}}}$

let the original no. be 10x + y

• Sum of 2 digits of 2 digit no. is 14

$\sf\implies x + y = 14$------( i )

• If the digits are reversed new no. is greater than the original no. by 36

$\sf\implies 36 + 10x + y = x + 10y$

$\sf\implies 36 + 10x - x + y - 10y = 0$

$\sf\implies 36 + 9x - 9y =$

$\sf\implies 9y - 9x = 36$

$\sf\implies y - x = 4$--------( ii )

• adding eq i and ii

$\sf\dag x + y + y - x = 14 + 4$

$\sf\dag 2y = 18$

$\sf\dag y = 9$

$\sf{\red{\boxed{\bold{\leadsto y = 8}}}}$

• putting value of y in eq . i

$\sf\dag x + y = 14$

$\sf\dag x + 9 = 14$

$\sf\dag x = 14 - 9$

$\sf\dag x = 5$

$\sf{\red{\boxed{\bold{\leadsto x = 5}}}}$

__________________________

$\longrightarrow 10x + y$

$\longrightarrow 10\times 5 + 9$

$\longrightarrow 50 + 9$

$\longrightarrow 59$

$\sf{\pink{\boxed{\bold{\leadsto Original\: no\: = \: 59 }}}}$

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$\sf{\bold{\green{\underline{\underline{Answer}}}}}$

• Original number is 59