Question

On a certain credit card, customers earn a percentage of their purchases back as rewards. The earned reward percentage is directly proportional to the average balance on the card. With an average balance of Rs $2000$, the reward percentage is $1.5\% $. What is the percentage with an average balance of Rs$2500$?

Answer 1

Hint: Here, the given question deals with two main concepts of mathematics that are- averages and percentages. In order to understand what the question means; students should be aware about the concept of averages and percentages. Here in this question, we have to find the reward percentage when the average balance is Rs$2500$.

Complete step-by-step solution:
Average is the mean value which equals the ratio of sum of the terms to the total number of terms.
$Average = \dfrac{{Sum\;of\;the\;terms}}{{Total\;number\;of\;terms}}$
The relative part which indicates hundredth parts of any quantity is called as percentage.
According to the question,
We are given that reward percentage is directly proportional to the average balance;
$\% \;earned = K\left( {Average\;balance} \right)$, we use the alphabet K to indicate direct proportionality.
Now, are also given that the $1.5\% $reward percentage is equal to the directly proportional average balance of Rs$2000$.
$
   \Rightarrow 1.5\% = K \times 2000 \\
   \Rightarrow K = \dfrac{{1.5\% }}{{2000}} \\
 $
So, we got the value of K, directly proportional.
The reward percentage when average balance is of Rs$2500$ is
$
   \Rightarrow \dfrac{{1.5\% }}{{2000}} \times 2500 \\
   \Rightarrow 1.875\% \\
 $

Therefore, the required reward percentage is $1.875\% $.

Note:The given question was an easy one. Students should know about averages and percentages a little bit. The only area of mistake in these types of questions is that the students misunderstand the question. Students should very carefully read the question and avoid making mistakes.