If ratio of C.I. & S.I. interest for same principal and rate of interest for 2 years is 1.2, rat

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6.Interest

hard

If the ratio of $C.I. \& S.I.$ interest for the same principal and rate of interest for $2$ years is $1.2,$ find the rate of interest (In $\%$)

$300$

$15$

$140$

$40$

Solution

Here, $C I=P\left[\left(1+\frac{R}{100}\right)^{2}-1\right]$

$=P\left[\left(1+\frac{R^{2}}{(100)^{2}}+\frac{2 R}{100}\right)-1\right]=\frac{P R}{100}\left[\frac{R}{100}+2\right]$

$\Rightarrow S I=\frac{P \times 2 \times R}{100} \Rightarrow \frac{C I}{S I}=1.2=\frac{\frac{P R}{100}\left[\frac{R+200}{100}\right]}{\frac{2 P R}{100}}$

$\Rightarrow \frac{ CI }{ SI }=\frac{200+ R }{200} \Rightarrow 1.2=\frac{200+ R }{200} \Rightarrow R =40 \%$

Standard 13

Quantitative Aptitude

The sample 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 (In $\%$)

medium

The difference between simple interest and compound interest compounded annually on a certain sum of money for $2$ years at $4 \%$ per annum is ₹ $1 .$ The sum (in ₹) is

medium

The compound interest (In ₹) on ₹ $800$ in $2 \frac{1}{2}$ years at $5 \%$ is

medium

Mr. Dua invested money in two schemes $A$ and $B$ offering compound interest at $8 \%$ per annum and $9 \%$ per annum respectively. If the total amount of ineterest accrued through two schemes together in two years was ₹ $4818.30$ and the total amount invested was ₹ $27000$ . What was the amount (In ₹) invested in scheme $A$.

hard

A sum of $Rs. 8448$ is to be divided between $X$ and $Y$ who are respectively $18$ and $19 \,yr$ old, in such a way that if their shares be invested at $6.25 \%$ per annum at compound interest, they will receive equal amounts on attaining the age of $21 \,yr$. The present share of $X$ is (In $Rs.$)

hard

If the ratio of $C.I. \& S.I.$ interest for the same principal and rate of interest for $2$ years is $1.2,$ find the rate of interest (In $\%$)

Solution

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