A two digit number is 4 times its sum of digits and 2 times the produc

1.	A two digit number is 4 times its sum of digits and 2 times the product of its digits. Find the number.
Answer» Let a two digit number be 10x + y, where y is unit place digit and x is tens place digit 10x + y = 4(x + y) ⇒ 10x + y = 4x + 4y ⇒ 6x – 3y = 0 ⇒ 2x = y …(i) and 10x + y = 2xy …(ii) Substituting y = 2x in (ii), we get 10x + 2x = 2x x 2x ⇒ 4x² – 12x = 0 ⇒ 4x(x – 3) = 0 ⇒ x = 0, 3 where x = 0, y = 0 when x = 3, y = 2 x 3 = 6 ∴ Required number is 10x + y = 10 x 3 + 6 = 36

A two digit number is 4 times its sum of digits and 2 times the product of its digits. Find the number.

Answer»

Let a two digit number be 10x + y, where y is unit place digit and x is tens place digit

10x + y = 4(x + y)

⇒ 10x + y = 4x + 4y

⇒ 6x – 3y = 0

⇒ 2x = y …(i)

and 10x + y = 2xy …(ii)

Substituting y = 2x in (ii), we get

10x + 2x = 2x x 2x

⇒ 4x² – 12x = 0

⇒ 4x(x – 3) = 0

⇒ x = 0, 3

where x = 0, y = 0

when x = 3, y = 2 x 3 = 6

∴ Required number is

10x + y = 10 x 3 + 6 = 36