Question

If a two digit number is 4 times the sum of its digit and three times the product of it digit, then find the number.

Answer 1

Let digit of ten and unit place are x and y respectively.

number = 10x + y

According to first condition

number = 4 × sum of digit

⇒ 10x + y = 4 × (x + y)

⇒ 10x + y = 4x + 4y

⇒ 10x – 4x = 4y – y

⇒ 6x = 3y

⇒ 2x = y

⇒ y = 2x …(i)

According to second condition number 

= 3 × Product of digit

10x + y = 3 × x × y

⇒ 10x + y = 3xy …(ii)

From equation (i) putting y = 2x in equation

10x + 2x = 3x × 2x

⇒ 12x = 6x²

⇒ 6x² – 12x = 0

⇒ 6x (x – 2) = 0

when 6x = 0, then x = 0

when x – 2 = 0, then x = 2

Hence, given number is two digit number,

so x ≠ 0 and hence x = 2

⇒ y = 2 × 2 = 4 [∵ y = 2x]

Hence, required number = 10x + y

= 10 × 2 + 4 = 24