Question

Box1 contains 500 marbles, 24% of which are black.Box2 contains some marbles of which 10% are black.You put the marbles together in another box and found that the percentage of black marble is 20%. How many medals were there in box 2?

A. 100
B.150
C. 200
D. 250
E. None of these

Answer 1

Let
`b_1` and
`b_2` denote the number of black marbles in box 1 and 2, respectively, and
`n_1` and
`n_2` the total number of marbles in box 1 and 2, respectively. Then

`(b_1)/(n_1)=(b_1)/(500)=24\%\implies b_1=120`

`(b_2)/(n_2)=10\%\implies10b_2=n_2`

`(b_1+b_2)/(n_1+n_2)=(120+b_2)/(500+n_2)=20\%\implies10(120+b_2)=2(500+n_2)`

`\implies600+5b_2=500+n_2`

`\implies5b_2=n_2-100`

Since
`b_2=(n_2)/(10)`, we have

`(5n_2)/(10)=n_2-100\implies1000=5n_2\implies n_2=200`

so there were 200 marbles in total in box 2 at the start.