Question

5. The product of the digits of a two-digit number
is 18. The number obtained by interchanging
the places of the digits is 63 less than the
original number. Find the original number.​

Answer 1

To Find :

• We need to find the original number.

Solution :

Let the units place digit be x and tens place digit be y.

• number formed = 10y + x

$\underline{ \large \purple{ \mathscr{\dag\:A \bf{ccourding} \: to \: \mathscr {Q} \bf{uestion} ....}}}$

The product of the digits of a two-digit number is 18.

• xy = 18 ....(1)

The number obtained by interchanging

the places of the digits is 63 less than the

original number.

• 10y + x - 63 = 10x + y

=> 10y - y = 10x - x + 63

=> 9y = 9x + 63

• Dividing both sides by 9

=> y - x = 7

=> y = 7 + x .....(2)

• putting value of x in equation 1)

=> xy = 18

=> x(7 + x) = 18

=> 7x + x² = 18

=> x² + 7x - 18 = 0

=> x² + 9x - 2x - 18

=> x(x + 9) - 2(x + 9)

=> (x + 9)(x - 2)

=> x = -9 , x = 2

• we will take positive value x = 2

• putting value of x in (2)

=> y - x = 7

=> y - 2 = 7

=> y = 9

• Original Number 10y + x

= 10 × 9 + 2

= 90 + 2

= 92

Hence,

• the original number is 92.

━━━━━━━━━━━━━━━━━━━━━━━━━

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀Done࿐

Answer 2

Answer:

Let the two digit number be xy.

According to the first condition.

xy = 18 ... (1)

According to the second condition.

» 10x + y - (10y + x) = 63

» x - y = 7 ... (2)

On squaring (2)

» (x - y)² = 49... (3)

Now, (x + y)² = (x - y)² + 4xy

= 49 + 72 = 121

i.e. (x + y) = 11 ... (4)

On solving (2) & (4), we get

x = 9 and y = 2

Therefore, the number is 92.