Question : A sum of INR 50,250 is divided into two parts such that the simple interest on the first part for $7 \frac{1}{2}$ years at $8 \frac{1}{3} \%$ p.a. is $\frac{5}{2}$ times the simple interest on the second part for $5 \frac{1}{4}$ years at $8 \%$ p.a. What is the difference (in INR ) between the two parts?
Option 1: 10,275
Option 2: 12,750
Option 3: 12,570
Option 4: 15,270
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Correct Answer: 12,750
Solution : Let the 1st part be $100x$ and the 2nd part be $100y$. According to the question, $\frac{100x \times \frac{15}{2} \times \frac{25}{3}}{100} = \frac{5}{2} \times \frac{100y \times \frac{21}{4} \times 8}{100}$ ⇒ $2 \times 62.5x = 5 \times 42y$ ⇒ $25x = 42y$ Ratio of $x : y = 42 : 25$ ⇒ $100x = 4200$ and $100y = 2500$ Total = 4200 + 2500 = 6700 Difference = 4200 – 2500 = 1700 Here, 6700 unit = INR 50250 Thus, 1700 unit = $\frac{50250}{6700} \times 1700$ = INR 12750 Hence, the correct answer is 12750.
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