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Minua uses 30% of her monthly earnings for rent and 50% of the remaining amount for food and transportation. If she spends dollar 525 for food and transportation, calculate how much she pays for rent.
\[\begin{align}
  & A.400\text{ dollar} \\
 & B.450\text{ dollar} \\
 & C.500\text{ dollar} \\
 & D.550\text{ dollar} \\
\end{align}\]

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Last updated date: 18th Jun 2024
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Answer
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Hint: In this question, we are given the percentage of spending of monthly earnings by Minua. We need to find the amount that she pays for rent using the given information. For this, we will first suppose monthly savings to be x. Then we will find the amount spent on rent using a given percentage of x in terms of x. Then we will use the second statement to form an equation and hence calculate the value of x which will be used to find the rent. We will use the formula $y\%\text{ of x}=\dfrac{y}{100}\times x$.

Complete step-by-step answer:
Let us suppose that, monthly salary of Minua is x dollars. We are given that, she spends 30% of her monthly earnings for rent. Hence, she spends 30% of x on rent. So, money spent on rent becomes equal to 30% of x.
As we know, y% of x can be written as $\dfrac{y}{100}\times x$.
Hence, money spent on rent $\Rightarrow \dfrac{30}{100}\times x=\dfrac{3}{10}x$.
Now we are given that, out of the rest of the money, 50% is spent on food and transportation. So let us find rest of money first.
Total money = Money on rent + Money not on rent.
Hence, rest of money $\Rightarrow x-\dfrac{3x}{10}$.
Taking LCM we get: $\Rightarrow \dfrac{10x-3x}{10}=\dfrac{7x}{10}$.
Hence, $\dfrac{7x}{10}$ money is left after payment of rent. Now, 50% of this money is used for food and transportation, so we can say 50% of $\dfrac{7x}{10}$ is spend on food and transportation.
\[\begin{align}
  & 50\%\text{ of }\dfrac{7x}{10}=\dfrac{50}{100}\times \dfrac{7x}{10} \\
 & \Rightarrow \dfrac{5}{10}\times \dfrac{7x}{10} \\
 & \Rightarrow \dfrac{7}{20}x \\
\end{align}\]
Hence, $\dfrac{7}{20}x$ money is spent on food and transportation.
We are also given that 525 dollar are spent on food and transportation. Therefore, $\dfrac{7}{20}x=525$.
Cross multiplying we get: $7x=10500$.
Dividing both sides by 7, we get: $x=\dfrac{10500}{7}=1500$.
Hence, Minua's monthly salary is 1500 dollar.
Since, amount spent on rent is $\dfrac{3}{10}x$ so we get:
$\Rightarrow \dfrac{3}{10}\times 1500=\left( 3\times 150 \right)=450\text{ dollars}$
Hence, the amount spent for rent is 450 dollar.

So, the correct answer is “Option B”.

Note: Students should note that, percentage of money spent on food and transportation is given for money after rent and not for whole month’s salary. They can make mistake of taking $\dfrac{50}{100}x$ as money for food and transportation. Take care of calculation while dealing with fractions.