Question

If A is increased by 20%, it equals B. If B is decreased by 50%, it equals C. Then ______% A is equal to C.

Answer 1

Hint: We will use the formula of gain amount and loss amount which is given as $gain=A+gain\%A$ and $loss=B-loss\%B$ . From this we will have 2 equations i.e. $A+20\%A=B$ and $B-50\%B=C$ . Then we will substitute the value of B from equation (1) into (2) because we want to find how much % of A is equal to B. On solving, we will get an answer.

Complete step-by-step answer:
Here, we are given that 20% increase in A is equal to B. So, we will use the formula as gain i.e. $=A+gain\%A$ . Similarly, there is 50% decrease in B and is equal to C, so we can write it as $loss=B-loss\%B$ .
Using the formula, we will get as
$A+20\%A=B$ ………………..(1)
$B-50\%B=C$ ………………………(2)
Now, we are asked to find what % of A is equal to C, so we want an equation in terms of A and C only. So, substituting value of B from equation (1) in equation (2). We will get as
$A+20\%A-50\%\left( A+20\%A \right)=C$
On further solving, we will get as
$A+\dfrac{20}{100}A-\dfrac{50}{100}\left( A+\dfrac{20}{100}A \right)=C$
$A+0.2A-0.5\left( A+0.2A \right)=C$
On doing simplification, we will get as
$1.2A-0.5\left( 1.2A \right)=C$
On multiplying the brackets, we will get
$1.2A-0.6A=C$
 $0.6A=C$
Thus, we can write it as $A\times \dfrac{60}{100}=C$ which means 60% A is equal to C.

Note: Remember the formula of increased in amount and decreased in amount. Sometimes students make mistakes in decreasing amount i.e. $loss=B+loss\%B$ instead of using the formula $loss=B-loss\%B$ . Thus, solving will get the wrong answer. So, do not make this mistake. Also, we can find B from equation (2) and then substitute it in equation (1) will get the same answer.