Harsh receives an inheritance of a certain 

amount from his grandfather. Of this he loses 32.5% in his 

effort to produce a film. From the balance, a taxi driver 

stole the sum of ` 1,00,000 that he used to keep in his 

pocket. Of the rest, he donated 20% to a charity. Further 

he purchases a flat in Ganga Apartment for ` 7.5 lakh. He 

then realises that he is left with only ` 2.5 lakh cash of his 

inheritance. What was the value of his inheritance?

Let Harsh's inheritance be \( x \) rupees.

### Step 1: Loss due to film production
Harsh loses 32.5% of his inheritance in his effort to produce a film. Therefore, after this loss, the remaining amount is:
\[
\text{Remaining after film production} = x - 0.325x = 0.675x
\]

### Step 2: Loss due to theft
A taxi driver stole ₹1,00,000 from the remaining amount. Therefore, the amount left after this theft is:
\[
\text{Remaining after theft} = 0.675x - 1,00,000
\]

### Step 3: Donation to charity
Harsh donates 20% of the remaining amount to charity. Therefore, the donation is:
\[
\text{Donation} = 0.20 \times (0.675x - 1,00,000)
\]
Thus, the amount left after the donation is:
\[
\text{Remaining after donation} = (0.675x - 1,00,000) - 0.20 \times (0.675x - 1,00,000)
\]
This simplifies to:
\[
\text{Remaining after donation} = 0.80 \times (0.675x - 1,00,000) = 0.54x - 80,000
\]

### Step 4: Purchase of a flat
Harsh purchases a flat for ₹7,50,000. Therefore, the amount left after the purchase is:
\[
\text{Remaining after flat purchase} = (0.54x - 80,000) - 7,50,000 = 0.54x - 8,30,000
\]

### Step 5: Final amount left
We are told that after all these expenses, Harsh is left with ₹2,50,000. Therefore, we can set up the equation:
\[
0.54x - 8,30,000 = 2,50,000
\]

### Step 6: Solve for \( x \)
Now, solve for \( x \):
\[
0.54x = 2,50,000 + 8,30,000
\]
\[
0.54x = 10,80,000
\]
\[
x = \frac{10,80,000}{0.54} = 20,00,000
\]

### Conclusion
The value of Harsh's inheritance was **₹20,00,000**.

Would you like further explanation on any part of this solution? Here are some related questions:

1. What would happen if Harsh donated 30% instead of 20% to charity?
2. How much money did Harsh lose in total due to theft and donations combined?
3. What is the percentage of his inheritance that Harsh spent on purchasing the flat?
4. If Harsh had saved the ₹1,00,000 that was stolen, how much would he have left after all the expenses?
5. What percentage of his total inheritance is Harsh left with?

**Tip:** Always double-check percentage calculations, as small errors can significantly impact your final answer.

Harsh receives an inheritance of a certain amount from his grandfather. Of this he loses 32.5% in his effort to produce a film. From the balance, a taxi driver stole the sum of ₹1,00,000 that he used to keep in his pocket. Of the rest, he donated 20% to a charity. Further he purchases a flat in Ganga Apartment for ₹7.5 lakh. He then realises that he is left with only ₹2.5 lakh cash of his inheritance. What was the value of his inheritance?

This detailed solution explains how to determine the value of Harsh's original inheritance after losing 32.5% in a film venture, theft of ₹1,00,000, donating 20% to charity, purchasing a flat for ₹7.5 lakh, and being left with ₹2.5 lakh. Ideal for students in Grades 9-11, the solution involves percentage loss, donations, and solving linear equations.

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