If \(\displaystyle \frac{1}{x}:\frac{1}{y}:\frac{1}{z}=2:3:5\), then \(x:y:z\) is equal to:
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 15 : 10 : 6
If the reciprocals are in the ratio 2 : 3 : 5, the numbers themselves are in the ratio of the reciprocals of 2, 3 and 5.
\(\displaystyle \frac{1}{x}=2k,\ \frac{1}{y}=3k,\ \frac{1}{z}=5k\)
\(\displaystyle x:y:z=\frac{1}{2}:\frac{1}{3}:\frac{1}{5}\)
Multiplying each term by 30 (the LCM of 2, 3 and 5): \(15:10:6\)
So \(x:y:z=\) 15 : 10 : 6.