Question

A two digit number is 4 times the sum of its digits and twice the product of the digits. Find the
numbers?
Ans:​

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

⇒

10/x + y/1=2

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

⇒

10/2y+ 1/y=2

⇒ 5/y+ 1/y=2

6/y=2

∴ y=3

⇒ x=2y=2(3)=6

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

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