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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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