Three varieties of rice taken in the ratio 3 : 4 : 5 are mixed. If 5 kg rice of first variety, 10 kg rice of second variety and some rice of third variety are added to the mixture, the ratio of the three varieties becomes 5 : 7 : 9. Find the quantity of the third variety of rice in the final mixture.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 90 kg
The quantities of the first two varieties are known in both mixtures, so they fix the size of the original mixture; the third variety then follows from the final ratio.
The original mixture (ratio 3 : 4 : 5):
Let the quantities be \(3k\), \(4k\) and \(5k\) kg
After the additions, the first two are \(3k+5\) and \(4k+10\) kg
Finding k (the first two now stand in the ratio 5 : 7):
\(\displaystyle \frac{3k+5}{4k+10}=\frac{5}{7}\)
\(21k+35=20k+50\)
\(k=15\)
The third variety in the final mixture:
First variety \(=3\times15+5=50\) kg, which is the 5 parts of 5 : 7 : 9, so one part = 10 kg
Third variety \(=9\times10=90\) kg (75 kg at the start and 15 kg added)