Basic Math MCQ 9 (Percent comparison , less or bigger than)
MCQ 9 : If y exceeds x by 20%, then x is less than y by_______?
a) 16% b) 16 1/3 % c) 16 2/3 % d) 16 3/5 %
Solution:
Here ‘y exceeds x by 20 %’ means if (suppose);
\[ x=z \]
then
\[ y=z+\frac{20z}{100}=\frac{120z}{100} \]
Now we suppose x is m% of y
i-e
\[ x = \frac{m}{100}\times y \]
\[ =\frac{m}{100}[\frac{120z}{100}] \]
But x=z
so,
\[ x=\frac{m}{100}[\frac{120x}{100}] \]
this gives
\[ m=\frac{10000}{120} = 83.333333333 \]
So x is 83.333333333% of y
Hence if y is 100 then x= 100-83.333333333= 16.666666667 or
\[ 16\frac{2}{3} \]
so x is 16.666666667% or \( 16\frac{2}{3} \) less than y
So option c is correct
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