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Question
A two digit number is 4 times the sum of its digit and twice the product of its digit. Find the number.
Solution
Let this two digit number be xy. Which means x=10x (as it comes in tens digit).
Then as per the question,
4(x+y)= 10x+y, ....... (i)
and 2(xy) =10x + y
⇒ 10x + y - 2xy = O ....... (ii)
From (i), we get: 6x = 3y
⇒ y = 2x
Putting this in (ii) , we get
10x + 2x - (2x) 2x = 0
⇒ 4x2 = 12x
⇒ 4x (x-3)=0
⇒ x=3, hence y=6
Hence the number is 36
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