A two-digit number is such that the product of its digits is 35. If 18

1.	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.
Answer» Let us consider, One’s digit of a two digit number = x and Ten’s digit = y The number is x + 10y By interchanging the digits, One’s digit = y and ten’s digit = x The number is y + 10x As per the statement, xy = 35 ………(1) And, x + 10y + 18 = y + 10x 18 = y + 10x – x – 10y x – y = 2 …(2) using algebraic identity: (x + y)²= (x – y)²+ 4xy (x + y)² = (2)² + 4(35) = 144 = (12)² Or x + y = 12 …(3) Subtracting (2) from (3), we get 2x =14 or x = 7 Form (1) : xy = 35 7(y) = 35 y = 5 Answer: The number is x + 10y = 7 + 10(5) = 57

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.

Answer»

Let us consider,

One’s digit of a two digit number = x and

Ten’s digit = y

The number is x + 10y

By interchanging the digits,

One’s digit = y and ten’s digit = x

The number is y + 10x

As per the statement,

xy = 35 ………(1)

And, x + 10y + 18 = y + 10x

18 = y + 10x – x – 10y

x – y = 2 …(2)

using algebraic identity: (x + y)²= (x – y)²+ 4xy

(x + y)² = (2)² + 4(35)

= 144

= (12)²

Or x + y = 12 …(3)

Subtracting (2) from (3), we get

2x =14

or x = 7

Form (1) : xy = 35

7(y) = 35

y = 5

Answer: The number is

x + 10y = 7 + 10(5) = 57