The price of a car is ₹ 3,25,000. It was insured to 85% of its price. The car was damaged completely in an accident and the insurance company paid 90% of the insurance. What was the difference between the price of the car and the amount received?

### Concept & Strategy This is a successive percentage application problem. The insurance payout is a percentage of the insured value, which itself is a percentage of the original price. We can track the total percentage of the car's original value that is *lost* to find the difference directly, rather than calculating absolute values at every single step. ### Step-by-step Solution **Given:** Original Price of car = ₹ 3,25,000 Insured percentage = 85% of original price Payout percentage = 90% of insured amount Let's calculate the actual amount received: $$ \text{Amount Received} = 90\% \text{ of } (85\% \text{ of Price}) $$ $$ \text{Amount Received} = 0.90 \times 0.85 \times 325000 $$ First, find the decimal multiplier: $$ 0.90 \times 0.85 = 0.765 $$ This means the owner received exactly 76.5% of the original car price. Now, calculate the difference between the original price (100%) and the amount received (76.5%). Percentage difference (loss) = $ 100\% - 76.5\% = 23.5\% $ Finally, calculate 23.5% of the original price to find the absolute monetary difference: $$ \text{Difference} = 23.5\% \text{ of } 325000 $$ $$ \text{Difference} = \frac{23.5}{100} \times 325000 = 23.5 \times 3250 $$ To calculate $ 23.5 \times 3250 $: $$ 23.5 \times 3250 = (20 + 3 + 0.5) \times 3250 $$ $$ = 65000 + 9750 + 1625 = 76375 $$ ### Exam Strategy & Shortcut Use **Unit Digit Estimation** combined with percentage logic. You need 23.5% of 325,000, which is $ 235 \times 325 $. The unit digit of $ 5 \times 5 $ is 5. Look at the options: (a) 32,500 (Ends in 0) (b) 48,750 (Ends in 0) (c) 76,375 (Ends in 5) (d) 81,250 (Ends in 0) Only Option C ends in 5. You don't even need to do the heavy multiplication! ### Common Pitfall A very common mistake is calculating the individual monetary values step-by-step ($325000 \times 0.85 = 276250$, then $276250 \times 0.9 = 248625$, then $325000 - 248625 = 76375$). While mathematically correct, it is a massive drain on time and introduces multiple points for calculation errors compared to combining the percentages first. ### Final Answer **Therefore, the correct answer is ₹ 76,375.**