Practice Simple Interest

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Calculate Simple Interest if

Principal \[(P)=Rs.3000\]
Amount \[(A)=Rs.3200\]

\[Rs.100\]

\[Rs.150\]

\[Rs.200\]

\[Rs.250\]

Simple Interest \[(SI)=A-P\]

\[=Rs.(3200-3000)\]

\[=Rs.200\]

Hence \[SI=Rs.200/-\]

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Calculate Principle if

Amount \[(A)=Rs.20800\]
Interest \[(SI)=Rs.100\]

\[Rs.20000\]

\[Rs.20300\]

\[Rs.20700\]

\[Rs.20900\]

Principle \[(P)=A-SI\]

\[=Rs.(20800-100)\]

\[=Rs.20700\]

Hence \[P=Rs.20700/-\]

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Calculate Amount if

Principal \[(P)=Rs.8000\]
Interest \[(SI)=Rs.50\]

\[Rs.7000\]

\[Rs.8000\]

\[Rs.7050\]

\[Rs.8050\]

Amount \[(A)=P+SI\]

\[=Rs.(8000+50)\]

\[=Rs.8050\]

Hence \[A=Rs.8050/-\]

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Simple Interest (SI) on a certain Amount is payable half-yearly. What is the Interest Rate (R) ?

\[\frac{R}{2}\]

\[\frac{R}{3}\]

\[\frac{R}{4}\]

\[\frac{R}{5}\]

When Interest is payable half-yearly, Interest Rate \[R\] will be \[\frac{R}{2}\]

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Simple Interest (SI) on a certain Amount is payable quarterly. What is the Interest Rate (R) ?

\[\frac{R}{2}\]

\[\frac{R}{3}\]

\[\frac{R}{4}\]

\[\frac{R}{5}\]

When Interest is payable quarterly, Interest Rate \[R\] will be \[\frac{R}{4}\]

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Simple Interest (SI) on a certain Amount is payable half-yearly. What is the Time Duration (T) ?

\[2T\]

\[3T\]

\[4T\]

\[5T\]

When Interest is payable half-yearly, Time Duration \[T\] will be \[2T\]

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Simple Interest (SI) on a certain Amount is payable quarterly. What is the Time Duration (T) ?

\[2T\]

\[3T\]

\[4T\]

\[5T\]

When Interest is payable quarterly, Time Duration \[T\] will be \[4T\]

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Calculate Simple Interest \[(SI)\] if

Principal \[(P)=Rs.400\]
Rate \[(R)=5\%\]
Time \[(T)=10 \ years\]

\[Rs.100\]

\[Rs.200\]

\[Rs.300\]

\[Rs.400\]

\[SI=\frac{P\times R\times T}{100}\]

\[=\frac{400\times 5\times 10}{100}\]

\[=200\]

Hence Simple Interest \[(SI)=Rs.200/-\]

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Calculate Principal \[(P)\] if

Simple Interest \[(SI)=Rs.6000\]
Rate \[(R)=3\%\]
Time \[(T)=5 \ years\]

\[Rs.10,000\]

\[Rs.20,000\]

\[Rs.30,000\]

\[Rs.40,000\]

\[P=\frac{SI\times 100}{R\times T}\]

\[=\frac{\left(6000\times 100\right)}{3\times 5}\]

\[=400\times 100\]

\[=40,000\]

Hence Principal \[(P)=Rs.40,000/-\]

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Calculate Interest Rate \[(R)\] if

Simple Interest \[(SI)=Rs.450\]
Principal \[(P)=Rs.5000\]
Time \[(T)=9 \ years\]

\[1\%\]

\[2\%\]

\[3\%\]

\[4\%\]

\[=\frac{SI\times 100}{P\times T}\]

\[=\frac{450\times 100}{5000\times 9}\]

\[=\frac{50\times 100}{5000}\]

\[=\frac{5000}{5000}\]

\[=1\%\]

Hence Interest Rate \[(I)=1\%\]

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Calculate Time Duration \[(T)\] if

Simple Interest \[(SI)=Rs.6400\]
Principal \[(P)=Rs.20000\]
Rate \[(R)=4\%\]

\[2 \ years\]

\[4 \ years\]

\[6 \ years\]

\[8 \ years\]

\[\frac{SI\times 100}{P\times R}\]

\[=\frac{6400\times 100}{20000\times 4}\]

\[=\frac{64}{8}\]

\[=8\]

Hence Time Duration \[(T)=8 \ years\]

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Simple Interest on a certain Amount for \[2\] years is \[Rs.50\]. Simple Interest on the same amount in \[5\] years will be __________

\[Rs.100\]

\[Rs.115\]

\[Rs.120\]

\[Rs.125\]

Simple Interest in \[2\] years \[=Rs.50\]

\[\therefore\] Simple Interest for \[1\] year \[=Rs.\frac{50}{2}=Rs.25\]

\[\therefore\] Simple Interest in \[5\] years \[=Rs.(25\times5)=Rs.125/-\]

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What sum of money must be given as simple interest for six months at \[4\%\] per annum in order to earn \[Rs.150\] interest?

\[Rs.6000\]

\[Rs.6500\]

\[Rs.7000\]

\[Rs.7500\]

\[P=\frac{\left(150\times 100\right)}{4\times 1}\times \frac{2}{1}\]

\[=Rs.7500\]

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A sum of money lent at simple interest amounts to \[Rs.880\] in \[2\] years and to \[Rs.920\] in \[3\] years. The sum of money (in rupees) is

\[Rs.600\]

\[Rs.700\]

\[Rs.800\]

\[Rs.900\]

If the principal be \[x\] and rate of interest be \[x\%\] per annum, then

SI after \[1\] year \[= 920 – 880 = Rs.40\]

\[\therefore\] SI after \[2\] years \[= Rs.80\]

\[\implies 880 = x + 80 \]

\[\implies x = (880 – 80)\]

\[= Rs.800\]

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The rate of simple interest per annum at which a sum of money doubles itself in \[16\frac{2}{3}\] years is

\[2\%\]

\[4\%\]

\[6\%\]

\[8\%\]

According to the question,

Principal \[= Rs. x\].

Interest \[= Rs. x \].

Time \[= 16\frac{2}{3}=\frac{50}{3}\] years

\[\therefore R=\left(\frac{SI\times 100}{P\times T}\right)\%\]

\[=\left(\frac{x\times 100}{x\times \frac{50}{3}}\right)\%\]

\[=\left(\frac{100\times 3}{50}\right)\%\]

\[=6\%\]

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The rate of simple interest per annum at which a sum of money doubles itself in \[16\frac{2}{3}\] years is

\[2\%\]

\[4\%\]

\[6\%\]

\[8\%\]

According to the question,

Principal \[= Rs. x\].

Interest \[= Rs. x \].

Time \[= 16\frac{2}{3}=\frac{50}{3}\] years

\[\therefore R=\left(\frac{SI\times 100}{P\times T}\right)\%\]

\[=\left(\frac{x\times 100}{x\times \frac{50}{3}}\right)\%\]

\[=\left(\frac{100\times 3}{50}\right)\%\]

\[=6\%\]

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Simple interest on a certain sum for \[6\] years is \[\frac{9}{25}\] of the sum. The rate of interest is

\[3\%\]

\[6\%\]

\[9\%\]

\[12\%\]

\[R=\left(\frac{SI\times 100}{P\times T}\right)\%\]

\[=\left(\frac{9\times 100}{25\times 6}\right)\%\]

\[=\left(\frac{9\times 4}{6}\right)\%\]

\[=6\%\]

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A sum of \[Rs.1550\] was lent partly at \[5\%\] and partly at \[8\%\] simple interest. The total interest received after \[3\] years is \[Rs.300\]. The ratio of money lent at \[5\%\] to that at \[8\%\] is :

\[Rs.420\]

\[Rs.580\]

\[Rs.840\]

\[Rs.960\]

According to question,

Interest of one year \[= 42\]
Rate \[= 5\%\]
Time \[= 1\] year

\[\therefore P=\frac{SI\times 100}{R\times T}\]

\[=\frac{42\times 100}{5\times 1}\]

\[=42\times 20\]

\[=Rs.840\]

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A sum of \[Rs. 4000\] is lent out in two parts, one at \[8\%\] simple interest and the other at \[10\%\] simple interest. If the annual interest is \[Rs. 352\], the sum lent at \[8\%\] is

\[Rs.6000\]

\[Rs.7000\]

\[Rs.8000\]

\[Rs.9000\]

Let the larger part of the sum be x

\[\implies\] Smaller part \[= (12000 – x )\]

According to the question,

\[\frac{\left(x\times 3\times 12\right)}{100}=\frac{\left(1200-x\right)x\times 9\times 16}{100}\]

\[\implies 36 x = (12000 – x ) 72 \]

\[\implies x = (12000 – x ) × 2\]

\[\implies x + 2 x = 24000 \]

\[\implies 3 x = 24000\]

\[x=\frac{24000}{3}\]

\[=Rs.8000\]

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The rate of interest per annum at which the total simple interest of a certain capital for \[1\] year is equal to the total simple interest of the same capital at the rate of \[5\%\] per annum for \[2\] years, is

\[4\%\]

\[6\%\]

\[8\%\]

\[10\%\]

According to the question

\[\frac{\left(P\times R\times 1\right)}{100}=\frac{\left(P\times 5\times 2\right)}{100}\]

[\[\because\] Capital is same in both cases]

\[r\times 1=5\times 2\]

\[\Rightarrow r=10\%\]