A sum of Rs. 1450 is lent in the beginning of a year at a certain rate of interest. After 8 months, another sum of Rs. 725 is lent but at a rate twice the former. At the end of the year, Rs. 67 is earned as interest from both the loans. What was the original rate of interest?
Solution
Correct Answer: Option E
Let the original rate of interest be R%.
Given, sum at the beginning of the year = Rs. 1450
We know that, Simple interest = (P × R × T)/100
∴S.I for 1 year on sum of Rs.1450 = (1450 × R × 1)/100
⇒ S.I1 = 14.5R …(1)
Also, money lent after 8 month = Rs. 725
Rate of interest on above loan = 2R
∴ S.I for 4 months on sum of Rs.725 \(= \frac{{725 \times 2R \times \left( {\frac{4}{{12}}} \right)}}{{100}}\)
S.I2 = (58R/12) ……(2)
Given sum of both simple interest at end of the year = Rs. 67
∴ 14.5R + 4.8R = 67
R = 3.47%
We find that the rate of interest doesn’t match any of the option. Hence, none of these.
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