CAT 2018 Quant Questions

Question:
There are two drums, each containing a mixture of paints A and B. In drum 1, A and B are in the ratio 18 : 7. The mixtures from drums 1 and 2 are mixed in the ratio 3 : 4 and in this final mixture, A and B are in the ratio 13 : 7. In drum 2, then A and B were in the ratio

229 : 141
220 : 149
239 : 161
251 : 163
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Correct Answer: 3

It is given that in drum 1, A and B are in the ratio 18 : 7.

Let us assume that in drum 2, A and B are in the ratio x : 1.

It is given that drums 1 and 2 are mixed in the ratio 3 : 4 and in this final mixture, A and B are in the ratio 13 : 7.

By equating concentration of A

\( \Rightarrow \) \(\frac{{3*\frac{{18}}{{18 + 7}} + 4*\frac{x}{{x + 1}}}}{{3 + 4}} = \frac{{13}}{{13 + 7}}\)

\( \Rightarrow \) \(\frac{{54}}{{25}} + \frac{{4x}}{{x + 1}} = \frac{{91}}{{20}}\)

\( \Rightarrow \) \(\frac{{4x}}{{x + 1}} = \frac{{239}}{{100}}\)

\( \Rightarrow \) \(x = \frac{{239}}{{161}}\)

Therefore, we can say that in drum 2, A and B are in the ratio \(\frac{{239}}{{161}}\) : 1 or 239 : 161.

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CAT 2018 Quant Questions
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