Question

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

​

Answer 1

Step-by-step explanation:

Let the digit in the ones place be x and tens place be y

Hence the two digit number =10y+x

Given that the two digit number =4 times sum of its digits

According to the question,

⇒ 10y+x=4(x+y)

⇒ 10y+x=4x+4y

⇒ 3x−6y=0

⇒ x=2y ------- ( 1 )

It is also given that the two digit number =2 times product of its digits

⇒ 10y+x=2xy

Divide by xy both the sides, we get

⇒

x

10

+

y

1

=2

Put x=2y from (1), we get

⇒

2y

10

+

y

1

=2

⇒

y

5

+

y

1

=2

⇒

y

6

=2

∴ y=3

⇒ x=2y=2(3)=6

⇒ The two digit number =(10y+x)=10(3)+6=36

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