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

239 : 161

Let the ratio of A and B in second drum = a : 1

Amount of A in the first drum = \(\frac{18}{18 + 7}\)

Amount of A in second drum = \(\frac{a}{a + 1}\)

Amount of A in final mixture = \(\frac{13}{13 + 7}\)

Use allegation,

\(\frac{13/20 \;- \;a/a+1}{7/100}\) = \(\frac{3}{4}\)

\(\frac{13}{20}\) - \(\frac{a}{a + 1}\) = \(\frac{21}{400}\)

\(\frac{13}{20}\) - \(\frac{21}{400}\) = \(\frac{a}{a + 1}\)

\(\frac{a}{a+ 1}\) = \(\frac{260 - 21}{400}\) = \(\frac{239}{400}\)

a = 239

1 = 400 - 239 = 161

Hence, ratio of A and B in second drum will be 239 : 161