Question : In an experiment, it was observed that metal A is 19 times heavier than water and metal B is 9 times heavier than water. In what ratio are metals A and B mixed so that the mixture thus obtained is 15 times heavier than water?
Option 1: 2 : 3
Option 2: 1 : 3
Option 3: 3 : 1
Option 4: 3 : 2
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Correct Answer: 3 : 2
Solution :
Let the ratio of metal A and metal B be $a:b$
Let the weight of water be 1 unit.
then the weight of metal A = 19 units
and, the weight of metal B = 9 units
According to the question,
$\frac{19a+9b}{a+b}=\frac{15}{1}$
⇒ $19a+9a=15(a+b)$
⇒ $19a + 9b =15a+15b$
⇒ $19a-15a=15a-9b$
⇒ $4a=6b$
⇒ $\frac{a}{b}=\frac{3}{2}$
$\therefore a:b=3:2$
Hence, the correct answer is 3 : 2.
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