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Question
A two digit number is four times the sum and 3 times the product of its digits, find the number.
Solution
Let this two digit number be 'Xi. Which means X=10x (as it comes in tens digit).
Then as per the question,
XY = 4 (X + Y)
⇒ 4(X+Y) = 10 X+ Y ..... (i)
and XY= 3(XY)= 10X + Y ..... (ii)
From (i), we get, 6X = 3Y
⇒ X = `"Y"/2`
Putting this in (ii) , we get : `(10 "Y")/2 + "Y" = (3 "Y")/2 xx "Y"`
`5"Y" + "Y" = 3/2 "Y"^2`
⇒ Solving this we get: 3Y2=12Y
⇒ Y = 4
Hence X = `"Y"/2 = 2`
Hence , number is 24.
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