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CAT 2018 Slot 2 — QA Question 13

AlligationEasy

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

Answer & solution

Correct answer: 239 : 161

  • A

    220 : 149

  • B

    251 : 163

  • C

    229 : 141

  • 239 : 161

Solution

Easy

Work with the fraction of A in each drum. Drum 1 has a known A-fraction; the final blend (drums 1 and 2 in ratio 3:43:4) has a known A-fraction. Set up one equation for the unknown A-fraction of drum 2, then read off A : B.

1

Fraction of A in each known mixture. In drum 1, A:B=18:7A:B=18:7, and in the final mixture A:B=13:7A:B=13:7.

Drum 1: f1=1818+7=1825Final: f=1313+7=1320\begin{aligned} &\text{Drum 1: } f_1=\frac{18}{18+7}=\frac{18}{25}\\ &\text{Final: } f=\frac{13}{13+7}=\frac{13}{20} \end{aligned}
2

Blend equation. Drums are mixed in ratio 3:43:4, so the final A-fraction is the weighted average of the two drum A-fractions. Let xx be drum 2's A-fraction.

3⋅1825+4x3+4=1320⇒ 3⋅1825+4x=7⋅1320(multiply by 7)⇒ 5425+4x=9120⇒ 4x=9120−5425=455−216100=239100⇒ x=239400\begin{aligned} &\frac{3\cdot \frac{18}{25}+4x}{3+4}=\frac{13}{20}\\ &\Rightarrow\ 3\cdot\frac{18}{25}+4x=7\cdot\frac{13}{20} \quad\text{(multiply by 7)}\\ &\Rightarrow\ \frac{54}{25}+4x=\frac{91}{20}\\ &\Rightarrow\ 4x=\frac{91}{20}-\frac{54}{25}=\frac{455-216}{100}=\frac{239}{100}\\ &\Rightarrow\ x=\frac{239}{400} \end{aligned}
3

Read off the ratio in drum 2. A-fraction is 239400\tfrac{239}{400}, so the B-fraction is 161400\tfrac{161}{400}.

A:B=239400:161400=239:161\begin{aligned} &A:B=\frac{239}{400}:\frac{161}{400}=239:161 \end{aligned}
A:B=239:161A:B=239:161

Take 700700 litres of final mix =300=300 (drum 1) +400+400 (drum 2). A in final =700⋅1320=455=700\cdot\tfrac{13}{20}=455; A from drum 1 =300⋅1825=216=300\cdot\tfrac{18}{25}=216. So A from drum 2 =239=239 out of 400400, i.e. 239:161239:161.

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CAT 2018 Slot 2 QA Q13: 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. — Solution | TheCATExam