Question

A two digit number is such that the product of its digits is 14. If 45 is added to the number, the digits interchange their places . Find the number .

Answer 1

go through the solution step by step

Answer 2

Answer:

Step-by-step explanation:

Solution :-

Let the tens place digit be x

And the units place digit be be 14/x

Number = 10x + 14/x

Interchanged number = 10 × 14/x + x

According to the Question,

⇒ 10x + 14/x + 45 = 10 × 14/x + x

⇒ 10x + 14/x + 45 = 140/x + x

⇒ 9x - 126/x + 45 = 0

⇒ 9x² + 45x - 126 = 0

Dividing equation by 9 , we get

⇒ x² + 5x - 14 = 0

By using factorization method, we get

⇒ x² + 7x - 2x - 14 = 0

⇒ (x² + 7) (x - 2) = 0

⇒ x = - 7, 2 (As x can't be negative)

⇒ x = 2

Number = 10x + 14/x = 10 × 2 + 14/2 = 20 + 14/2 = 27

Hence, the required number is 27.