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Amit earns $\$32000$ per month. He spends \[\dfrac{1}{4}\] of his income on food. \[\dfrac{3}{10}\] of the remainder on house rent and \[\dfrac{5}{21}\] of the remainder on the education of children. How much money is still left with him?

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Last updated date: 13th Jun 2024
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Answer
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Hint: First we should find the income spent by Amit on food. Now we should find the income spent by Amit on house rent. Now again we should find the income spent by Amit on education of children.

Complete step-by-step answer:
From the question, we were given that Amit earns $\$32000$ per month. We were also given that he spends \[\dfrac{1}{4}\] of his income on food. \[\dfrac{3}{10}\] of the remainder on house rent and \[\dfrac{5}{21}\] of the remainder on the education of children. We know that the money left with Amit is equal to the difference of $\$32000$ and the sum of income spent by Amit on food, house rent and education of children.

So, now we will find the amount spent by Amit on food.
Income spend by Amit on food \[=\$\left(\dfrac{1}{4}\times32000\right)=\$8000\]
Now we will find the amount spent by Amit on house rent.
Income spend by Amit on house rent \[=\$\left(\dfrac{3}{10}\times32000\right)=\$9600\]
Now we will find the amount spent by Amit on the education of children.
Income spend by Amit on education of children \[=\$\left(\dfrac{5}{21}\times32000\right)=\$7619.04\]
We already know that Amit earns $\$32000$ per month.
From the question, we were given to find the money still left with him.
The money left with Amit is equal to the difference of $\$32000$ and the sum of income spent by Amit on food, house rent and education of children.
\[\Rightarrow \]Money left with Amit\[=\$32000-\left(\$8000+\$9600+\$7619.04\right)=\$6780.96\].
So, it is clear that the money left with Amit is equal to $\$6780.96$.

Note: Students should have a clear understanding how to solve this problem. First of all, we should understand the question in a correct manner because if a small mistake is made, then we cannot find the correct answer. Students should also avoid calculation mistakes while solving this problem.