Question

Question 51

In questions 24 to 59, fill in the blanks to make the statements true.
If A is increased by 20 %, it equals B. If B is decreased by 50%, it equals C. Then, ___ % of A is equal to C.

Answer 1

Given, if A is increased by 20%, then it is equal to B.
$\therefore$ A + 20 % of A = B
$\Rightarrow A(1+\frac{20}{100})=B\Rightarrow \frac{120}{100}A=B\Rightarrow B=\frac{6}{5}A............\left(i\right)$
If B is decreased by 50%, then it is equal to C.
$\therefore$ B - 50 % of B = C
$\Rightarrow B(1-\frac{50}{100})=C\Rightarrow B\times \frac{50}{100}=C\Rightarrow \frac{1}{2}B=C\Rightarrow B=2C..........\left(ii\right)$
On comparing Eqs. (i) and (ii), we get
$\frac{6}{5}A=2C\Rightarrow \frac{A}{C}=\frac{10}{6}\Rightarrow C=\frac{6}{10}A\Rightarrow C=\frac{3}{5}A$
$\therefore$ In percentage, $\frac{C}{A}\times 100=\frac{\frac{3}{5}A}{A}\times 100\%=\frac{3}{5}\times 100\%=60\%$
Hence, 60 % of A is equal to C.