Question

In a 2 digit number sum of digits is 10 and their product is 16 find the number

Answer 1

Answer:

Let the digit at unit place be x. Then digit at ten's digit = (10 - x).

∴ Original number = 10(10 - x) + x

= 100 - 10x + x

= 100 - 9x

According to the question ;

x(10 - x) = 16

⇒ 10x - x² - 16 = 0

⇒ x² - 10x + 16 = 0

⇒ x² - 8x - 2x + 16 = 0

⇒ x(x - 8) - 2(x - 8) = 0

⇒ (x - 8)(x - 2) = 0

⇒ x = 8 or x = 2

Hence, Original number = 82.