CAT Quantitative Aptitude Questions | CAT Percentages Problems - Variables

The question is from CAT Percentages. 2IIMs CAT question bank provides you with CAT questions that can help you gear for CAT Exam CAT 2023. This is a very interesting question from the topic percentages using Variables.In this question, we are given a bucket with a certain % of large and small balls along with certain % of different colours and we need to find the total no. of balls. It may seem to be a tough one to crack but its a simple, when you understand the concept.

Question 23 : A bucket has ‘a’ number of small and large balls out of which b% are black. Of the small balls, c% are black and of large balls, d% are black. Find the number of small balls in the bucket.

1. a * \\frac{(b - d)}{c + b - d}\\)
2. a * \\frac{(b - d)}{c + b - 2d}\\)
3. a * \\frac{(c - b)}{b - d}\\)
4. a * \\frac{(b - d)}{c - d}\\)

Explanatory Answer

Method of solving this CAT Question from Percentages: Form the equations carefully and you are through!

Let the number of small and large balls be S and L respectively
=> a = S + L ------- Equation(1)
Also, b% of a = c% of S + d% of L
=> ba = cS + dL
=> ba = cS + d(a - S) (Putting L = a – S from Equation(1))
=>( b – d) * a = (c – d) * S
=> S = a * \\frac{(b - d)}{c - d}\\)

The question is " Find the number of small balls in the bucket.

Hence, the answer is a * \\frac{(b - d)}{c - d}\\)

Choice D is the correct answer.