Question

the two digit number is 5 times the sum of digit is also equal to 5 more than that which product of

Answer 1

Let the digits in the units place and ten's place be x and y respectively.
∴ Number = 10 × y + x = 10y + x
Given, Number = 5 × Sum of the digits
∴ 10y + x = 5 (x + y)
⇒ 10y + x = 5x + 5y
⇒ 5y = 4x
Given,
Number = 2 × Product of digit + 5
∴ 10y + x = 2xy + 5
⇒ 8x2 + 25 = 45x
⇒ 8x2 – 45x + 25 = 0
⇒ 8x2 – 40x – 5x + 25 = 0
⇒ 8x(x – 5) – 5(x – 5) = 0
⇒ (x – 5) (8x – 5) = 0
⇒ x – 5 = 0 or 8x – 5 = 0
⇒ x = 5 or
∴ x = 5                         (
Digit cannot be fraction)
When x = 5
∴ Number = 10y + x = 10 × 4 + 5 = 40 + 5 = 45
Thus, the number is 45.