A box contains 400 marbles, of which 40% are blue. You pick some marbles of which 25% are blue. Of the remaining marbles, 50% are blue marbles. How many marbles did you pick?

Question: A box contains 400 marbles, of which 40% are blue. You pick some marbles of which 25% are blue. Of the remaining marbles, 50% are blue marbles. How many marbles did you pick?

Solution:
Given that,
Total marbles = 400
Blue marbles initially = 40% of 400 = (40/100) × 400 = 160
Non-blue marbles = 400 - 160 = 240

Let the number picked be x.
∴ Blue picked = 25% of x = 0.25x
and non-blue picked = 0.75x

And,
Remaining marbles = 400 - x
∴ Remaining blue marbles = 160 - 0.25x

ATQ, Of the remaining marbles, 50% are blue then we get,
160 - 0.25x = 0.5(400 - x)
⇒ 160 - 0.25x = 200 - 0.5x
⇒ 0.5x - 0.25x = 200 - 160
⇒ 0.25x = 40
⇒ x = 40/0.25
∴ x = 160

So the number of marbles you picked is 160.