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

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answer is B.

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Detailed Solution

It is given that the two-digit number is 4 times the sum of its digits and twice the product of its digits.
Let us assume that the number in tens place be

x

and in units place be

y

.
Then, the number will be 10x+y.
Since, the two-digit number is 4 times the sum of its digit.
Then,

⇒ 10 x + y = 4 (x + y) ⇒ 6 x − 3 y = 0 ⇒ y = 2 x .... (1)

Since, two-digit number is twice the product of its digits.
Thus,

⇒ 10 x + y = 2 x y ⇒ 10 x + 2 x = 2 x y ⇒ 12 x = 2 x y ⇒ y = 6

Substituting the value of y in the equation (1).
Then,

⇒ y = 2 x ⇒ 6 = 2 x ⇒ x = 3

Hence, the number is,

= 10 x + y = 10 (3) + 6 = 30 + 6 = 36

The number is 36.
Hence, the correct option is 2.

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