Question

A two digit is such that the product of the digits is 18.when 63 is substracted from the number,the digits interchange their places.​

Answer 1

${ \huge{ \underline{ \underline{ \sf{ \green{GivEn : }}}}}}$

• Product of digits = 18

• When 63 is subtracted from the number ,the digits interchange their places.

${ \huge{ \underline{ \underline{ \sf{ \green{To \: find :}}}}}}$

• What's the number?

${ \huge{ \underline{ \underline{ \sf{ \green{SoluTion : }}}}}}$

Let the unit place digit and ten's digit number be y and x respectively.

According to the question :-

The number will be = 10x + 18/x

Given that,

product of digits = 18

Therefore,

⟶ xy = 18

⟶ y = 18/x..............(1)

Again, it's given that

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

Therefore,

⟶ (10x + y)- 63 = 10y + x

⟶ 9x - 9y = 63

⟶ x - y = 7.............eq(2)

Now, put y = 18/x in eq(2)

⟶ x -8 /x = 7

⟶ x² - 18 = 7x

⟶ x² - 7x - 18 = 0

⟶ x² - 9x + 2x - 18 = 0

⟶ x(x - 9)+ 2( x - 9) = 0

⟶ (x -9)(x+2) = 0

⟶ x = 9 Or, x = -2

( -2 is not appropriate)

Now, put the value of x in eq (1)

⟶ y = 18/x

⟶ y = 2

Therefore, the number will be

= 10x + 18/x

= 10 × 9 + 18/9

= 92