3) A basket contains a mix of red and white ball. If you pick out one white ball

Question

3) A basket contains a mix of red and white ball. If you pick out one white ball in random, then the number of red balls in the basket becomes 2 more than the number of white balls. Now if you add 5 more white balls (the white ball that was taken outside earlier is put back inside) into the basket and now you pick a red ball, you see that the basket now has a total of 13 balls. How many red balls were originally there in the basket? [25 points] b) 4 d) None of the above e) Cannot be determined without knowing the initial ball count of at least one type

Explanation / Answer

Answer: c). 5

Explanation: Let the number of red balls are R and number of whicte balls are W. Now, let T be the total number of balls inside the basket. Then,

T=R+W ------------------------------------------ (1)

If one white ball is picked out, then number of whilte balls in the baset=W-1 and the number of Red balls will remain the same i.e. R. Now, since, red balls becomes 2 more than white balls. So,

R=(W-1)+2

R=W+1 ---------------------------------------------- (2)

Now, if we add 5 more white balls. so, no. of white balls in the basket=W+5 and after picking one red ball, the no. of red balls in the basket will be=R-1. Now, since total no. of balls =13. So,

(W+5)+(R-1)=13

W+R+4=13

W+R=13-4

W+R=9 ------------------------------------------------------ (3)

Substituting R=W+1 from eqn 2 into eqn 3

W+W+1=9

2W+1=9

2W=9-1=8

W=8/2

W=4 ---------------------------------------------- (4)

Now, substituting W=4 into eqn 2.

R=4+1

R=5

Hence, there were 5 red balls inside the basket.

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