A tempo is insured to the extent of $ \frac{4}{5} $ of its original value. If the premium on it at the rate of 1.3 percent amounts to ₹ 910, the original value of the tempo is

### Concept & Strategy This question tests consecutive percentage applications. The premium is calculated based on the *insured value*, not the original value. The insured value is a fraction of the original value. $$ \text{Premium} = \text{Premium Rate} \times \text{Insured Value} $$ $$ \text{Insured Value} = \text{Fraction Insured} \times \text{Original Value} $$ ### Step-by-step Solution **Given:** Insured portion = $ \frac{4}{5} $ of original value. Premium rate = 1.3% = $ \frac{1.3}{100} $. Total premium paid = ₹ 910. Let the original value of the tempo be $x$. Determine the insured value in terms of $x$: $$ \text{Insured Value} = \frac{4}{5}x $$ Set up the equation based on the premium calculation: $$ 1.3\% \text{ of Insured Value} = 910 $$ $$ \frac{1.3}{100} \times \left( \frac{4}{5}x \right) = 910 $$ Simplify the equation to solve for $x$: Convert 1.3 to $ \frac{13}{10} $ to remove decimals: $$ \left( \frac{13}{1000} \right) \times \left( \frac{4}{5}x \right) = 910 $$ $$ \frac{52}{5000}x = 910 $$ Isolate $x$: $$ x = \frac{910 \times 5000}{52} $$ Simplify the fraction. Notice that 910 and 52 share common factors: $$ x = \frac{910}{52} \times 5000 $$ Divide 910 by 13 to get 70, and 52 by 13 to get 4: $$ x = \frac{70}{4} \times 5000 $$ $$ x = 17.5 \times 5000 $$ $$ x = 87500 $$ ### Exam Strategy & Shortcut Instead of complex fractions, use a reverse multiplier approach mentally. The premium is 1.3%, meaning the insured value is $ 910 \div 0.013 $. $ 910 \div 0.013 = 910000 \div 13 = 70000 $. So, the insured value is 70,000. We know $ \frac{4}{5} $ of original = 70,000. This means 4 parts = 70,000. 1 part = $ 70,000 \div 4 = 17,500 $. 5 parts (Original value) = $ 17,500 \times 5 = 87,500 $. ### Common Pitfall The most common trap is assuming the 1.3% premium applies to the *original* value of the tempo directly, completely ignoring the $ \frac{4}{5} $ insurance constraint. This would lead to incorrectly solving $ 1.3\% \times x = 910 $, yielding 70,000 (which isn't even an option, leading to panic). ### Final Answer **Therefore, the correct answer is ₹ 87,500.**