Question

Meeta saves Rs 400 from her salary. If this is 10% of her salary, what is her salary?

Answer 1

Hint: We assume the salary of Meeta as $x$ rupees and express her savings in terms of $x$ using the given percentage in the question that is 10%. We equate the expression in $x$ to the given saving amount in the question that is 400 rupees and solve for $x$.

Complete step-by-step answer:
We know that the percentage in mathematics is a number or ratio expressed as a fraction of 100. If we have $a$ number of elements and there are total $b$ number of elements then we can express $a$ as a percentage $p$ of $b$ using the working rule,
\[p=\dfrac{a}{b}\times 100\]
We know that when we say $p%$ it means there are $p$ number of items out of every 100 items. When we say $p%$ of $a$ it means $p$ number of items can be allocated if we divide $a$ into hundred. The number of items in $p%$ of $a$ are $\dfrac{p}{a}\times 100$. \[\]

Let us assume that the salary of Meeta is $x$ rupees. We are given the question that she saves $S=400$ rupees from her salary and the saving amount is 10% of the whole salary. She saves 10% salary. So the amount of salary in terms of $x$ is 10% of $x$ that is
\[S=\dfrac{10}{100}x=\dfrac{1}{10}x\]
We are given that $S=400$. So we have
\[\dfrac{1}{10}x=400\]
We cross multiply to have,
\[\begin{align}
  & 1\times x=10\times 400 \\
 & \Rightarrow x=4000 \\
\end{align}\]
So the salary of Meeta is found to be 4000 rupees. \[\]

Note: We note that we have assumed that she does not have any additional spending. We can also find her total expenses as percentage of salary as $\dfrac{x-S}{x}\times 100$.We note that $a%$of $b$ is equal to $b%$ of $a.$ and $a$ is greater than $b$ by percentage $\dfrac{a-b}{b}\times 100$.