Question

19. A number say z is exactly the four times the sum of its digits and twice the product of the digits. Find the numbers.

Answer 1

Let the no. z be 10x + y

10x + y = 4 (x + y)

10x + y = 4x + 4y

6x - 3y = 0

2x - y = 0 eq1

10x + y = 2xy eq2

From eq1 y = 2x put y in eq2

10x + 2x = 2xy

12x = 2xy

y = 12x / 2x = 6

Put value of y in eq1

2x - 6 = 0

x = 6/2 = 3

No. was 10x + y

= 10×3 + 6

= 36


Thanks

Answer 2

Let the digit in the ones place be x and tens place be y Hence the two digit number = 10y + x Given that the two digit number = 4 times sum of its digits ⇒ 10y + x = 4(x + y) ⇒ 10y + x = 4x + 4y ⇒ 3x – 6y = 0 ⇒ 3x = 6y ∴ x = 2y → (1) It is also given that the two digit number = 2 times product of its digits ⇒ 10y + x = 2xy Divide by xy both the sides, we get ∴ y = 3 Hence x = 6 The two digit number is (10y + x) = 10(3) + 6 = 36