lf two digit number is four times the sum of its digits and twice the product of digits. Find the number.

Options

A. `36`
B. `63`
C. `42`
D. `24`

Answer

A

Explanation

Let the ten's digit of the required number be x and its unit's digit be y .
Then , ` 10 x + y = 4 ( x + y ) rArr 6 x - 3y = 0 rArr 2 x - y = 0 " " `… (i)
Also, ` 10 x + y = 2xy " " `… (ii)
Putting ` y = 2x ` from (i) in (ii), we get
`10 x + 2x = 4x ^(2) rArr 4x ^(2) - 12 x = 0 `
` " " rArr 4x ( x- 3) =0`
` " " rArr x - 3 = 0 rArr x = 3 " " [because ` ten's digit, ` x ne 0 ]`.
Putting ` x = 3 ` in (i), we get `y = 6 `.
Thus, ten's digit = 3 and unit's digit = 6.
Hence, the required number is 36.