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 the total value of Harsh's inheritance be denoted by \( x \).

### Step 1: Loss due to film production
Harsh loses 32.5% of his inheritance in his effort to produce a film, which leaves him with:
\[
\text{Remaining after film loss} = x - 0.325x = 0.675x
\]

### Step 2: Loss due to theft
After that, a taxi driver stole ` ₹1,00,000 `. This leaves him with:
\[
\text{Remaining after theft} = 0.675x - 1,00,000
\]

### Step 3: Donation to charity
Harsh then donates 20% of the remaining amount to charity. The remaining amount before donation is \( 0.675x - 1,00,000 \), and 20% of this amount is:
\[
\text{Donation} = 0.2 \times (0.675x - 1,00,000)
\]
The remaining amount after donation is:
\[
\text{Remaining after donation} = (0.675x - 1,00,000) - 0.2 \times (0.675x - 1,00,000) = 0.8 \times (0.675x - 1,00,000)
\]

### Step 4: Purchase of the flat
He then purchases a flat for ₹7.5 lakh. After this, he is left with ₹2.5 lakh cash. So the remaining amount after the flat purchase is:
\[
0.8 \times (0.675x - 1,00,000) - 7,50,000 = 2,50,000
\]

### Step 5: Solve the equation
Now, we solve the equation:
\[
0.8 \times (0

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 realizes that he is left with only ₹2.5 lakh cash of his inheritance. What was the value of his inheritance?

Learn how to solve a real-life inheritance problem involving percentage loss, theft, donation, and property purchase. Follow a detailed step-by-step solution to find the initial value of the inheritance. Suitable for students in Grades 9-12.

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