There are two drums, each containing a mixture of gels A and B. In the first drum, A and B are in the ratio 18 : 7. The mixtures from the first and second drums are mixed in the ratio 3 : 4 by volume, and in this final mixture A and B are in the ratio 13 : 7. In the second drum, A and B were in the ratio:
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 239 : 161
Take 3 litres from the first drum and 4 litres from the second, making 7 litres. The quantity of gel A in the final 7 litres is known from 13 : 7, so the A coming from the second drum can be found.
A in 3 litres of the first drum \(\displaystyle =3\times\frac{18}{25}=\frac{54}{25}\)
A in the final 7 litres \(\displaystyle =7\times\frac{13}{20}=\frac{91}{20}\)
A in 4 litres of the second drum \(\displaystyle =\frac{91}{20}-\frac{54}{25}=\frac{455-216}{100}=\frac{239}{100}\)
B in those 4 litres \(\displaystyle =4-\frac{239}{100}=\frac{161}{100}\)
In the second drum, A : B \(=\) 239 : 161.
Why the other options are incorrect
Option (2) 161 : 239 — Incorrect. It is the ratio B : A, the reverse of what is asked.
Option (3) 239 : 400 — Incorrect. It is the ratio of A to the whole mixture of the second drum, not A : B.
Option (4) 161 : 400 — Incorrect. It is the ratio of B to the whole mixture of the second drum.