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The simple interest on a sum of money for 3 years is ₹240 and the compound interest on the same sum, at the same rate for 2 years is ₹170. The rate of interest is:

Solution

✅ Correct Option: 4

Simple interest is the same amount every year.

SI for 1 year=2403=₹80\text{SI for 1 year}=\dfrac{240}{3}=₹80

SI for 2 years=₹160\text{SI for 2 years}=₹160


Compound interest for 2 years is ₹170.

The extra 170−160=₹10170-160=₹10 is nothing but the interest earned on the first year's interest of ₹80.

So,

10=r100×8010=\dfrac{r}{100}\times80

⇒r=10×10080\Rightarrow r=\dfrac{10\times100}{80}

⇒r=12.5\Rightarrow r=12.5

Rate=1212%\text{Rate}=12\dfrac{1}{2}\%

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