Question

A's expenditure is $20\%$ more than B's expenditure. B's expenditure is $30\%$ less than C's expenditure. By what percentage is A's expenditure less than C's expenditure?

• A. $16\%$
• B. $12\%$
• C. $14\%$
• D. $18\%$

Answer 1

The correct option is A $16\%$

Let A's expenditure be x
So B's expenditure be y and C's be z
Now, $x=y+\frac{20}{100}y=\frac{6}{5}y\therefore y=\frac{5}{6}x$
Also, $y=z-\frac{30}{100}z=\frac{7}{10}z\Rightarrow \frac{5}{6}x=\frac{7}{10}z\Rightarrow z=\frac{50}{42}x=\frac{25}{21}x$
So, A's expenditure is less than C's by
$\frac{\frac{25}{21}x-x}{{\left(\frac{25}{21}\right)}^x}\times 100=\frac{4}{25}\times 100=16\%$