Question : If $P =\frac{96}{95\times97}, Q = \frac{97}{96\times98}$ and $R = \frac{1}{97}$, then which of the following is true?
Option 1: $P < Q < R $
Option 2: $R < Q < P $
Option 3: $Q < P < R $
Option 4: $R < P < Q $
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Correct Answer: $R < Q < P $
Solution :
$P = \frac{96}{95 \times 97} = \frac{1}{95} \times \frac{96}{97}$
$Q = \frac{97}{96 \times 98} = \frac{1}{96} \times \frac{97}{98}$
$R = \frac{1}{97}$
Comparing $P$ and $R$,
$\frac{1}{95}\times\frac{96}{97} > \frac{1}{97}⇒P > R$.
Comparing $P$ and $Q$,
$\frac{1}{95}\times\frac{96}{97} > \frac{1}{96}\times \frac{97}{98}⇒P > Q$.
Comparing $Q$ and $R$,
$\frac{1}{96} \times \frac{97}{98}> \frac{1}{97}⇒Q > R$.
Hence, the correct answer is $R<Q<P$.
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