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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Question : A sum of Rs. 5,000 is divided into two parts such that the simple interest on the first part for $4 \frac{1}{5}$ years at $6 \frac{2}{3} \%$ p.a. is double the simple interest on the second part for $2 \frac{3}{4}$ years at 4% p.a. The ratio of the second part to the first part is:
Option 1: 11:14
Option 2: 11 : 13
Option 3: 14 : 11
Option 4: 13 : 11
Question : Money was lent on simple interest. After 12 years, its simple interest becomes $\frac{3}{5}$ of the money. Find the rate of interest.
Option 1: 4% p.a.
Option 2: 2% p.a.
Option 3: 5% p.a.
Option 4: 3% p.a.
Question : If the simple interest at the same rate of interest on INR 500 for 4 years and INR 700 for 2 years combined, is INR 280, then what is the rate of interest?
Option 1: $9 \frac{3}{17}\%$
Option 2: $6 \frac{5}{17}\%$
Option 3: $8 \frac{4}{17}\%$
Option 4: $7 \frac{3}{17}\%$
Question : The simple interest on a certain sum for 3 years at 14% p.a. is INR 4,200 less than the simple interest on the same sum for 5 years at the same rate. Find the sum.
Option 1: INR 16,000
Option 2: INR 10,000
Option 3: INR 15,000
Option 4: INR 12,000
Question : The compound interest (compounding annually) on a certain sum at the rate of 8% per annum for two years is INR 6,656. What would be the simple interest on the same sum at the same rate of interest for two years?
Option 1: INR 5,600
Option 2: INR 6,224
Option 3: INR 6,400
Option 4: INR 6,336
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