Question

A two - digit number is such that the product of its digits is 20. If 9 is added to the number, the digits interchange their places. Find the number.

Answer 1

Let the one’s digit be ‘a’ and ten’s digit be ‘b’.

Given, two - digit number is such that the product of its digits is 20.

⇒ ab = 20 ----- (1)

Also,

If 9 is added to the number, the digits interchange their places.

⇒ 10b + a + 9 = 10a + b

⇒ a – b = 1 ----- (2)

Substituting value of a from eq1 in to eq2

⇒ 20/b – b = 1

⇒ b² + b – 20 = 0

⇒ (b + 5)(b – 4) = 0

Thus,

b = 4 and a = b + 1 = 5

Number is 45.