Question

Linear Equations in Two Variables
153
16. A two-digit number is such that the product of its digits is 35. If 18
is added to the number, the digits interchange their places. Find the
number
CBSE 2006​

Answer 1

Answer:

57 is the number

Explanation

Let the original number = xy

Products of the digits = 35

xy = 35

y = 35/x ..... (1)

If 18 is added to the number, the digits interchange their places.

Original number = xy = 10x + y

Number formed by interchanging the digits = yx = 10y + x

According to the question:

⟹ 10x + y + 18 = 10y + x

⟹ 10x + y + 18 - 10y - x = 0

⟹ 9x - 9y + 18 = 0

⟹ 9 ( x - y + 2 ) = 0

⟹ x - y + 2 = 0/9

⟹ x - y + 2 = 0

From (1)

⟹ x - (35/x) + 2 = 0

⟹ x²/x - 35/x + 2x/x = 0

⟹ ( x² - 35 + 2x)/x = 0

⟹ x² - 35 + 2x = 0

⟹ x² + 2x - 35 = 0

⟹ x² + 7x - 5x - 35 = 0

⟹ ( x + 7)(x - 5 ) = 0

Now,

⟹ x + 7 = 0

⟹ x = -7

or

⟹ x - 5 = 0

⟹ x = 5

As, digits of a number can not be negative, 5 is the value of x.

x = 5

y = 35/x = 35/5 = 7

The number is xy = 57