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
Correct Answer: 3
Let the ratio of A and B in drum 2 be x : 1
Applying alligation,
$\frac{13}{20}-\frac{x}{x+1}=\frac{3}{4}=>\frac{13}{20}-\frac{x}{x+1}=\frac{3}{4} \times \frac{72-65}{100}=\frac{21}{400}$
$=>\frac{x}{25}-\frac{13}{20}=\frac{13}{20}-\frac{21}{400}=\frac{239}{400}$
$=>400 x=239 x+239$
$x=239 / 161$
Required ratio is 239 : 161.
Let the ratio of A and B in drum 2 be x : 1
Applying alligation,
$\frac{13}{20}-\frac{x}{x+1}=\frac{3}{4}=>\frac{13}{20}-\frac{x}{x+1}=\frac{3}{4} \times \frac{72-65}{100}=\frac{21}{400}$
$=>\frac{x}{25}-\frac{13}{20}=\frac{13}{20}-\frac{21}{400}=\frac{239}{400}$
$=>400 x=239 x+239$
$x=239 / 161$
Required ratio is 239 : 161.
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