Averages , Ratio and Proportion Question 8 - CAT 2021
Question
A box has 450 balls, each either white or black, there being as many metallic white balls as metallic black balls. If 40% of the white balls and 50% of the black balls are metallic, then the number of non-metallic balls in the box is:
Step-by-Step Explanation
Let the total number of white balls be W and black balls be B.
W + B = 450 --- (Equation 1)
- Equate the metallic counts:
We are given that the number of metallic white balls equals the number of metallic black balls:
40% of W = 50% of B
0.4W = 0.5B
W = 1.25B
- Solve for the individual totals:
Substitute W = 1.25B into Equation 1:
1.25B + B = 450
2.25B = 450
B = 200
W = 450 − 200
= 250
- Calculate the number of non-metallic balls:
Non-metallic White = 60% of 250 = 150
Non-metallic Black = 50% of 200 = 100
Total Non-metallic Balls = 150 + 100 = 250
Correct Answer: 250
💡 FundaMakers Tip:
Total non-metallic percentage tracks directly as the complement of metallic counts. If the total metallic sum is 100 + 100 = 200 balls, subtracting this value from the total pool of 450 balls gives the non-metallic count of 250 instantly.