Question

a two digit number is four times the sum and three times the product of its digits.find the number

Answer 1

if x is ones digit and y is tens then no. is
10y + x
10y + x = 4 (x + y)
10y + x = 3xy
two equqtions two variables now solve easily

Answer 2

Let the tens digit be x and the units digit be y.

Then the two-digit number is (10x + y).

Given: Two-digit number = 4 times sum of its digits

⇒10x + y = 4(x + y)

⇒ 10x + y = 4x + 4y

⇒ 6x = 3y

… (1)

Given: Two-digit number = Twice the product of its digits

⇒ 10x + y = 2(xy)

⇒10x + y – 2xy = 0 … (2)

Substituting from equation (1) in equation (2), we get



⇒5y + y – y2 = 0

⇒y2 – 6y = 0

⇒y (y – 6) = 0

⇒ y = 0 or y – 6 = 0

We reject y = 0 because then x would also be zero.

Therefore, y = 6

Substituting this value of y in equation 1, we get



Hence, the required number is (10 × 3 + 6) = 36.