The percentage errors in quantities $P, Q, R$ and $S$ are $0.5\%,\,1\%,\,3\%$ and $1 .5\%$ respectively in the measurement of a physical quantity $A\, = \,\frac{{{P^3}{Q^2}}}{{\sqrt {R}\,S }}$ . the maximum percentage error in the value of $A$ will be $........... \%$
JEE MAIN 2018, Diffcult
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Maximum percentage error in $A$
$=3(\%$ error in $p)+2(\%$ error in $Q)+\frac{1}{2}(\%$ error in $R)+1(\% $ error in $S)$
$=3 \times 0.5+2 \times 1$
$=\frac{1}{2} \times 3+1 \times 1.5$
$=1.5+2+1.5+1.5$
$=6.5 \%$
$=3(\%$ error in $p)+2(\%$ error in $Q)+\frac{1}{2}(\%$ error in $R)+1(\% $ error in $S)$
$=3 \times 0.5+2 \times 1$
$=\frac{1}{2} \times 3+1 \times 1.5$
$=1.5+2+1.5+1.5$
$=6.5 \%$
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