Question

2 digit no is 4 time sum of its digits and twice the product of its digits find no

Answer 1

Hi friend !
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let ones digit no x 
then tens digit no is 10 x
original no is x+10x
ATQ 4(x+10x) = x+10x
also 2(10x^2) = x+10x
      20 x^2      = x + 10 x
20x^2-11x      =0 
x(20x-11)        =0 
x=0 
or 
x=11/20 
no is 11/20 + 10X11/20
 121/20 

Answer 2

let tens place be y and ones place be x
then the two digit number = 10y+x    (eg: 54 where, y is 5 and x is 4,∴5×10+4=54)

according to the first condition,
10y+x = 4(x+y) and, ................................ (i)

10y+x = 2(xy) ...........................................(ii)

∴ from (i) and (ii), 4(x+y) = 2(xy)

⇒4x+4y = 2xy

4y/y = 2x - 4x
 
⇒4 = -2x

-2x = 4

x = 4+2 ⇒ x= 6 
now substituting x= 6 in (ii)
 10y + 6 = 2×6 y
10y + 6 = 12y
10y-12y = -6
⇒ -2y = -6
 y = -6/-2 ⇒ 6/2 = 3
∴ the two digit number is 36
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