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.

- a * \\frac{(b - d)}{c + b - d}\\)
- a * \\frac{(b - d)}{c + b - 2d}\\)
- a * \\frac{(c - b)}{b - d}\\)
- a * \\frac{(b - d)}{c - d}\\)

a * \\frac{(b - d)}{c - d}\\)

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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. **

Choice D is the correct answer.

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