Ravindra has three times as much money as Aravinda does. If Ravindra gives a quarter of his money to Aravinda, then Aravinda will have Rs 80 less than Ravindra. How much money does Aravinda start with?

Let's denote the amount of money that Aravinda initially has as \( x \). 

Ravindra initially has three times as much money as Aravinda, so he has \( 3x \).

According to the problem, Ravindra gives a quarter of his money to Aravinda. After giving a quarter of his money, Ravindra will have:
\[
3x - \frac{1}{4} \times 3x = 3x - \frac{3x}{4} = \frac{12x}{4} - \frac{3x}{4} = \frac{9x}{4}
\]

Aravinda, after receiving the quarter of Ravindra's money, will have:
\[
x + \frac{3x}{4} = \frac{4x}{4} + \frac{3x}{4} = \frac{7x}{4}
\]

It is given that after this transaction, Aravinda will have Rs 80 less than Ravindra. Therefore, we have the equation:
\[
\frac{7x}{4} = \frac{9x}{4} - 80
\]

To solve for \( x \), subtract \( \frac{7x}{4} \) from both sides:
\[
0 = \frac{9x}{4} - \frac{7x}{4} - 80
\]
\[
0 = \frac{2x}{4} - 80
\]
\[
0 = \frac{x}{2} - 80
\]

Now, multiply both sides by 2 to solve for \( x \):
\[
x = 160
\]

So, Aravinda initially had Rs 160.

Would you like more details or have any questions?

Here are 5 related questions to consider:
1. What would the initial amount be if Ravindra had twice as much money as Aravinda?
2. How would the problem change if Ravindra gave half of his money instead of a quarter?
3. What if Aravinda had Rs 100 less than Ravindra after the transfer?
4. How would the situation be different if Ravindra gave money to a third person instead?
5. How can we generalize this problem for any ratio between Ravindra's and Aravinda's initial amounts?

**Tip:** When dealing with word problems, always define your variables clearly and translate the given conditions into equations step by step.

Learn how to solve a word problem involving money distribution between Ravindra and Aravinda. Understand the steps to find Aravinda's initial amount based on the given conditions. Suitable for students in Grades 7-9.

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