A sum of money at simple interest amounts to Rs. 14,160 in 3 years. If the rate of interest is increased to 25%, the same sum amounts to Rs. 14,700 in the same time. The rate of interest is 5% $5 \frac{1}{2}$ 6% 7%
A sum of money at simple interest amounts to Rs. 14,160 in 3 years. If the rate of interest is increased to 25%, the same sum amounts to Rs. 14,700 in the same time. The rate of interest is
A$\text{5%}$
B$5 \frac{1}{2}$
C$\text{6%}$
D$\text{7%}$
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Correct answer is: 6%
Explanation:\(\Large P+\frac{Pr \times 3}{100} = 14160\)
\(\Large P + P \times \frac{5r}{400} \times 3 = 14700\)
\(\left[ Rate\ of\ Int. = r + \frac{25}{100} r \right]\)
(By Ii) and (ii)
\(\Large P + \frac{5}{4} \left(14160-P\right)\)
\(=> 4P + 70800 - 5P = 58800\)
\(=> P = 70800 - 58800 - 12000\)
\(\text{Therefore, From equation (i),}\)
\(\Large 12000+\frac{12000 \times r \times 3}{100}\)
\(\Large 120 \times 3 \times r = 14160 - 12000 = 2160\)
\(=> \Large r = \frac{2160}{120 \times 3}\)
\(r = 6 \text{%}\)
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