Question

A two digits no. is 4 times the sum of its digits and twise the product of digits

Answer 1

let the 2 digit no. be xy (here xy is not x×y but xy=10x + y)
xy=4 (x+y) -------- [1]
xy=2×x×y---------- [2]

in equation [1]
10x+y= 4x + 4y
10x-4x=4y-y
6x=3y
6x-3y=0
y=2x --------------[3]

in equation [2]
10x+y=2×x×y ------------- [4]

substitute [3] in [4]
10x+2x=2×x×2x
12x =4x^2
... (after solving)
x=0 & x=3


substitute x=0in [3]
y=0

substitute x=3 in [3]
y=6

therefore,
Number = xy = 36
(remember x=0,y=0 is not possible because the number is 2 digit)



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Hope it helps!