CAT 1999 | Question: 69

Question

Three labelled boxes containing red and white cricket balls are all mislabelled. It is known that one of the boxes contains only white balls and another one contains only red balls. The third contains a mixture of red and white balls. You are required to correctly label the boxes with the labels red, white and red and white by picking a sample of one ball from only one box. What is the label on the box you should sample?

• A. white
• B. red
• C. red and white
• D. Not possible to determine from a sample of one ball

Answer 1

Answer is C

Suppose the boxes are mislabelled as below

R box labelled as W

W labelled as RW

RW labeled as R

Now if we choose a ball from box labeled R we get a W ball. However we can't determine if the box contains only W or a mixture of RW. Same case with if we choose ball from box labeled W

Now if we choose a ball from box labeled RW, we get a W balls. Here we know that the box will contain only W balls (as the box is mislabeled as RW it will surely not contain RW balls). Similarly if we get a R ball, we are sure it contains only R balls. Now we can conclude the correct labels of other two boxes too, as no box is correctly labeled.

Answer 2

Any one of A, B, C could be the answer

Say the box contain White ball lebel as WR

               "         "       Red   "    "      "   W

               "        "     WhiteRed "  "     "   R

 

If u put up a ball from box lebel R and the color of ball also Red

Then it must not be box of Red ball (As all boxes are mislabeled)

------->The box is filled up with WhiteRed

Next we have 2 boxes, and one box lebel White

---------> This box is filled up with Red balls (As it is also mislebeled and We already marked up WhiteRed Box)

----------> Last box must be filled up with White balls

Similarly in other approach too we get the correct result