Subject: General Aptitude · Chapter: Ratio and Proportion · Exam: 2006 · Marks: · Difficulty:
In a mixture of three varieties of tea, the ratio of their weights is 4 : 5 : 8. If 5 kg tea of the first variety, 10 kg tea of the second variety and some quantity of tea of the third variety are added to the mixture, the ratio of the weights of three varieties of tea becomes 5 : 7 : 9. Find the quantity of the third variety of tea in the final mixture.
Answer
Answer (as printed):
Explanation
Let the weights of 1st, 2nd and 3rd varieties of tea in the original mixture be $4x, 5x$ and $8x$ kg respectively. Then, $\frac{4x+5}{5x+10}=\frac{5}{7} \Leftrightarrow 7(4x+5)=5(5x+10) \Leftrightarrow 28x+35=25x+50 \Leftrightarrow 3x=15 \Leftrightarrow x=5$. So, the weights of 1st, 2nd and 3rd varieties in the original mixture are 20 kg, 25 kg and 40 kg respectively. Let $y$ kg of third variety be added. Then, $\frac{25+10}{40+y}=\frac{7}{9} \Leftrightarrow 7(40+y)=9\times35 \Leftrightarrow 40+y=\frac{9\times35}{7}=45 \Leftrightarrow y=5$. Hence, quantity of third variety in the final mixture $=(40+5)$ kg $=45$ kg.
Explanation as extracted from the printed page; notation may be imperfect.