Cant the problem be done like this :

Let the initial total no of marbles be x 'Given 60% of them are red which means 3x/5 of the marbles are red

Later 20 marbles are added out of which 3 are red which means total marble count is x+20 and total red marble count is 3x/5+3= (3x+15)/5

given (3x+15)/5(x+20)=50/100

=>6x+30=5x+100
=>x=70 the ans sud be 70 ?

70 is correct value for x. But x represents red marbles before addition of 20, question asked for new value. So x+20 = 70+20 = 90

I made the same mistake.

Here's another method.
If initial 60 percent is converted to 50 percent upon adding 15 percent of red, then the fraction of 15 percent red collection is 2/9.
Now 15 percent of 2/9 of total is 3.
i.e
3/20 * 2/9 * x = 3
So x = 90

Initial number of marbles = Y

Initial number of red marbles =60/100Y = 3/5Y
Number of non red marbles = 40/100y = 2/5Y

If 20 marbles added and 3 goes to red = 3/5Y + 3

Non red = 2/5Y + 17
If new red marbles in jar is 50% let new number of marbles be X
So X/2 =3/5Y + 3
Non red will be
X/2 = 2/5Y + 17
Simultaneous equation becomes
5X - 4Y = 170
5X - 6Y = 30
Y = 70
substituting for Y gives new number of red and non red marbles to be 45
Answer = 90.

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