Question

A two digit number is such that the product of its digits is 18.When 63 is subtracted from the number, the digits interchange their places. Find the number ​

Answer 1

Answer:

Answer is 92.

Let the number be 10x+y

According to question,

   10x+y−63=10y+x

⇒10x−x+y−10y=63

⇒9x−9y=63

⇒x−y=7

⇒x=7+y   (i)

xy=18 (ii)

Substituting the value of x in (ii) we get,

  (7+y)y=18

⇒y2+7y−18=0

⇒y2+9y−2y−18=0

⇒y(y+9)−2(y+9)=0

⇒(y+9)(y−2)=0

⇒y=−9 and y=2

y=−9 is not valid

∴y=2

Putting the value of y in (i) we get,

 x−2=7

⇒x=7+2

⇒x=9

So the number =10x+y=10(9)+2=92

Hope this helps you

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Answer 2

$\Large\underline\mathbf{Given:-}$

• The product of the digits of a two digit number is 18.
• When 63 is subtracted from the original number, the digits interchange their places.

$\Large\underline\mathbf{To \: Find:-}$

• What is the original number ?

$\Large\underline\mathbf{Solution:-}$

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

$\large{\boxed{\bf{\: NUMBER = 10x + y\: }}}$

CASE:- 1)

✧ The product of the digits of a two digit number is 18

${\underline{\bf{According \: To \: Question:-}}}$

➠ xy = 18...❶

CASE:- 2)

✧ When 63 is subtracted from the original number, the digits interchange their places

❮ Reversed Number = 10y + x ❯

${\underline{\bf{According \: To \: Question:-}}}$

➠ 10x + y –63 = 10y + x

➠ 10x + y –10y –x = 63

➠ 9x –9y = 63

Take common '9' from both sides

➠ x –y = 7

➠ x = 7 + y...❷

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

➠ (7 + y)y = 18

➠ 7y + y² = 18

➠ y² +7y –18 = 0

➠ y² +(9 –2)y –18 = 0

➠ y² +9y –2y –18 = 0

➠ y(y +9) –2(y +9) = 0

➠ (y –2) (y +9) = 0

${\underline{\underline{\bf{\star y = -9 \: (Neglected) \: \star}}}}$

${\underline{\underline{\bf{\star \: y = 2 \: \star}}}}$

Put the value of 'y' in equation 2), we get

➠ x = 7 + 2

${\underline{\underline{\bf{\star \: x = 9 \: \star}}}}$

❒ NUMBER = 10x + y

❒ NUMBER = 10(9) + 2

$\large{\boxed{\bf{\star \: NUMBER = 92\: \star}}}$

❝ Hence, the number formed is 92 ❞

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