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