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Simple Interest
1.

कितने वर्षों में 12% वार्षिक दर से 3000 रु का साधारण ब्याज 1080 हो जाएगा -

2.Find the simple interest on Rs. 5200 for 2 years at 6% per annum.

Explanation:

Solution:

3.Rs. 1200 is lent out at 5% per annum simple interest for 3 years. Find the amount after 3 years.

Explanation:

Solution:
$\begin{array}{rl}& A=P+I\\ & A=1200+\left(\frac{PTR}{100}\right)\\ & A=\left[1200+\left(\frac{1200×5×3}{100}\right)\right]\\ & \text{Amount},\phantom{\rule{thinmathspace}{0ex}}A=Rs.\phantom{\rule{thinmathspace}{0ex}}1380\end{array}$

4.Interest obtained on a sum of Rs. 5000 for 3 years is Rs. 1500. Find the rate percent.

Explanation:

Solution:
$\begin{array}{rl}& \text{Let}\phantom{\rule{thinmathspace}{0ex}}\text{rate}\phantom{\rule{thinmathspace}{0ex}}\text{is}\phantom{\rule{thinmathspace}{0ex}}R\mathrm{%}\\ & \text{We}\phantom{\rule{thinmathspace}{0ex}}\text{have},\\ & I=\frac{PTR}{100}\\ & \text{Here},\phantom{\rule{thinmathspace}{0ex}}1500=5000×3×R\\ & \text{Thus},\phantom{\rule{thinmathspace}{0ex}}R=10\mathrm{%}\end{array}$

5.Find the difference between the simple interest and the compound interest at 5% per annum for 2 years on principal of Rs. 2000.

Explanation:

Solution:
$\begin{array}{rl}& \text{The}\phantom{\rule{thinmathspace}{0ex}}\text{difference}\phantom{\rule{thinmathspace}{0ex}}\text{between}\phantom{\rule{thinmathspace}{0ex}}\text{compound}\phantom{\rule{thinmathspace}{0ex}}\text{interest}\phantom{\rule{thinmathspace}{0ex}}\text{and}\\ & \text{simple}\phantom{\rule{thinmathspace}{0ex}}\text{interest}\phantom{\rule{thinmathspace}{0ex}}\text{over}\phantom{\rule{thinmathspace}{0ex}}\text{two}\phantom{\rule{thinmathspace}{0ex}}\text{years}\phantom{\rule{thinmathspace}{0ex}}\text{is}\phantom{\rule{thinmathspace}{0ex}}\text{given}\phantom{\rule{thinmathspace}{0ex}}\text{by}\\ & \frac{{Pr}^{2}}{{100}^{2}}\phantom{\rule{thinmathspace}{0ex}}or\phantom{\rule{thinmathspace}{0ex}}P{\left(\frac{r}{100}\right)}^{2}\\ & \text{Here,}\phantom{\rule{thinmathspace}{0ex}}\text{Principal}\phantom{\rule{thinmathspace}{0ex}}\left(P\right)=Rs.\phantom{\rule{thinmathspace}{0ex}}2000\\ & \text{Rate}\phantom{\rule{thinmathspace}{0ex}}\left(r\right)=5\mathrm{%}\\ & \text{Now}\phantom{\rule{thinmathspace}{0ex}}\text{difference},\\ & D=\frac{\left(2000×5×5\right)}{\left(100×100\right)}\\ & D=Rs.\phantom{\rule{thinmathspace}{0ex}}5\end{array}$

6.Find the rate of interest if the amount after 2 years of simple interest on a capital of Rs. 1200 is Rs. 1440.

Explanation:

Solution:
$\begin{array}{rl}& \text{Amount},\phantom{\rule{thinmathspace}{0ex}}A=Rs.\phantom{\rule{thinmathspace}{0ex}}1440\\ & \text{Principal},\phantom{\rule{thinmathspace}{0ex}}P=Rs.\phantom{\rule{thinmathspace}{0ex}}1200\\ & \text{Interest},\phantom{\rule{thinmathspace}{0ex}}I=Rs.\phantom{\rule{thinmathspace}{0ex}}\left(1440-1200\right)=240\\ & R=\frac{\left(240×100\right)}{\left(1200×2\right)}=10\mathrm{%}\\ & \\ & \text{Alternatively},\\ & \text{We}\phantom{\rule{thinmathspace}{0ex}}\text{can}\phantom{\rule{thinmathspace}{0ex}}\text{go}\phantom{\rule{thinmathspace}{0ex}}\text{through}\phantom{\rule{thinmathspace}{0ex}}\text{a}\phantom{\rule{thinmathspace}{0ex}}\text{thought}\phantom{\rule{thinmathspace}{0ex}}\text{process}\phantom{\rule{thinmathspace}{0ex}}i.e.\\ & 1200\phantom{\rule{thinmathspace}{0ex}}--20\mathrm{%}↑\left(240\phantom{\rule{thinmathspace}{0ex}}\text{in}\phantom{\rule{thinmathspace}{0ex}}2\phantom{\rule{thinmathspace}{0ex}}\text{years}\right)-->1400\\ & \text{That}\phantom{\rule{thinmathspace}{0ex}}\text{means}\phantom{\rule{thinmathspace}{0ex}}10\mathrm{%}\phantom{\rule{thinmathspace}{0ex}}\text{rise}\phantom{\rule{thinmathspace}{0ex}}\text{in}\phantom{\rule{thinmathspace}{0ex}}\text{each}\phantom{\rule{thinmathspace}{0ex}}\text{year}\end{array}$

7.What is the difference between the simple interest on a principal of Rs. 500 being calculated at 5% per annum for 3 years and 4% per annum for 4 years?

Explanation:

Solution:
$\begin{array}{rl}& {I}_{1}=\frac{P{T}_{1}{R}_{1}}{100}\\ & {I}_{1}=\frac{\left(500×3×5\right)}{100}=Rs.\phantom{\rule{thinmathspace}{0ex}}75\\ & {I}_{1}=\frac{P{T}_{2}{R}_{2}}{100}\\ & {I}_{2}=\frac{\left(500×4×4\right)}{100}=Rs.\phantom{\rule{thinmathspace}{0ex}}60\\ & \text{Difference}=Rs.\phantom{\rule{thinmathspace}{0ex}}5\\ & \\ & \text{Alternatively},\\ & \text{The}\phantom{\rule{thinmathspace}{0ex}}\text{interest}\phantom{\rule{thinmathspace}{0ex}}\text{is}\phantom{\rule{thinmathspace}{0ex}}\text{calculated}\phantom{\rule{thinmathspace}{0ex}}\text{simply}\phantom{\rule{thinmathspace}{0ex}}\text{and}\phantom{\rule{thinmathspace}{0ex}}\text{then}\phantom{\rule{thinmathspace}{0ex}}\text{it}\phantom{\rule{thinmathspace}{0ex}}\text{will}\phantom{\rule{thinmathspace}{0ex}}\text{have}\phantom{\rule{thinmathspace}{0ex}}\\ & \text{a}\phantom{\rule{thinmathspace}{0ex}}\text{rise}\phantom{\rule{thinmathspace}{0ex}}\text{of}\phantom{\rule{thinmathspace}{0ex}}15\mathrm{%}\phantom{\rule{thinmathspace}{0ex}}\text{in}\phantom{\rule{thinmathspace}{0ex}}{1}^{st}\phantom{\rule{thinmathspace}{0ex}}\text{case}\phantom{\rule{thinmathspace}{0ex}}\text{and}\phantom{\rule{thinmathspace}{0ex}}16\mathrm{%}\phantom{\rule{thinmathspace}{0ex}}\text{in}\phantom{\rule{thinmathspace}{0ex}}{2}^{nd}\phantom{\rule{thinmathspace}{0ex}}\text{case}.\\ & \text{Difference}=1\mathrm{%}\phantom{\rule{thinmathspace}{0ex}}\text{on}\phantom{\rule{thinmathspace}{0ex}}500=Rs.\phantom{\rule{thinmathspace}{0ex}}5\\ & \\ & \text{Otherwise},\phantom{\rule{thinmathspace}{0ex}}\\ & 500--15\mathrm{%}↑-->575\phantom{\rule{thinmathspace}{0ex}}\left({1}^{st}\phantom{\rule{thinmathspace}{0ex}}\text{case}\right)\\ & 500--16\mathrm{%}↑-->580\phantom{\rule{thinmathspace}{0ex}}\left({2}^{nd}\phantom{\rule{thinmathspace}{0ex}}\text{case}\right)\\ & \text{We}\phantom{\rule{thinmathspace}{0ex}}\text{can}\phantom{\rule{thinmathspace}{0ex}}\text{see}\phantom{\rule{thinmathspace}{0ex}}\text{clear}\phantom{\rule{thinmathspace}{0ex}}\text{difference}\phantom{\rule{thinmathspace}{0ex}}\text{of}\phantom{\rule{thinmathspace}{0ex}}Rs.\phantom{\rule{thinmathspace}{0ex}}5\end{array}$

8.What is the simple interest on a sum of Rs. 700 if the rate of interest for the first 3 years is 8% per annum and for the last 2 years is 7.5% per annum?

Explanation:

Solution:
$\begin{array}{rl}& {1}^{st}\phantom{\rule{thinmathspace}{0ex}}\text{case}:\\ & {I}_{1}=\frac{700×3×8}{100}=Rs.\phantom{\rule{thinmathspace}{0ex}}168\\ & {2}^{nd}\phantom{\rule{thinmathspace}{0ex}}\text{case}:\\ & {I}_{2}=\frac{700×2×7.5}{100}=Rs.\phantom{\rule{thinmathspace}{0ex}}105\\ & \text{Then}\phantom{\rule{thinmathspace}{0ex}}\text{total}\phantom{\rule{thinmathspace}{0ex}}\text{interest}\phantom{\rule{thinmathspace}{0ex}}\text{for}\phantom{\rule{thinmathspace}{0ex}}\text{five}\phantom{\rule{thinmathspace}{0ex}}\text{years}\\ & =\left({I}_{1}+{I}_{2}\right)=Rs.\phantom{\rule{thinmathspace}{0ex}}273\\ & \\ & \text{Alternatively},\\ & \text{As}\phantom{\rule{thinmathspace}{0ex}}\text{interest}\phantom{\rule{thinmathspace}{0ex}}\text{is}\phantom{\rule{thinmathspace}{0ex}}\text{calculated}\phantom{\rule{thinmathspace}{0ex}}\text{as}\phantom{\rule{thinmathspace}{0ex}}\text{simple}\phantom{\rule{thinmathspace}{0ex}}\text{interest}\phantom{\rule{thinmathspace}{0ex}}\\ & \text{so}\phantom{\rule{thinmathspace}{0ex}}\text{we}\phantom{\rule{thinmathspace}{0ex}}\text{can}\phantom{\rule{thinmathspace}{0ex}}\text{add}\phantom{\rule{thinmathspace}{0ex}}\text{up}\phantom{\rule{thinmathspace}{0ex}}\text{rates}\phantom{\rule{thinmathspace}{0ex}}\text{for}\phantom{\rule{thinmathspace}{0ex}}\text{all}\phantom{\rule{thinmathspace}{0ex}}\text{given}\phantom{\rule{thinmathspace}{0ex}}\text{5}\phantom{\rule{thinmathspace}{0ex}}\text{years}\phantom{\rule{thinmathspace}{0ex}}\text{and}\phantom{\rule{thinmathspace}{0ex}}\\ & \text{calculate}\phantom{\rule{thinmathspace}{0ex}}\text{it}\phantom{\rule{thinmathspace}{0ex}}\text{easily}\phantom{\rule{thinmathspace}{0ex}}i.e.\\ & \text{For}\phantom{\rule{thinmathspace}{0ex}}\text{the}\phantom{\rule{thinmathspace}{0ex}}\text{five}\phantom{\rule{thinmathspace}{0ex}}\text{years}\phantom{\rule{thinmathspace}{0ex}}\text{rate}\\ & =\left(8×3+7.5×2\right)=39\mathrm{%}\\ & \text{Now},\\ & 700--39\mathrm{%}↑-->973\\ & \text{Interest}=Rs.\phantom{\rule{thinmathspace}{0ex}}273\\ & \text{The}\phantom{\rule{thinmathspace}{0ex}}\text{thought}\phantom{\rule{thinmathspace}{0ex}}\text{can}\phantom{\rule{thinmathspace}{0ex}}\text{go}\phantom{\rule{thinmathspace}{0ex}}\text{this}\phantom{\rule{thinmathspace}{0ex}}\text{way,}\phantom{\rule{thinmathspace}{0ex}}\text{we}\phantom{\rule{thinmathspace}{0ex}}\text{internally}\phantom{\rule{thinmathspace}{0ex}}\text{calculated}\phantom{\rule{thinmathspace}{0ex}}\\ & 10\mathrm{%}\phantom{\rule{thinmathspace}{0ex}}\text{of}\phantom{\rule{thinmathspace}{0ex}}700=\left(\frac{700}{10}\right)=70.\\ & \text{Then},\phantom{\rule{thinmathspace}{0ex}}39\mathrm{%}\phantom{\rule{thinmathspace}{0ex}}\text{of}\phantom{\rule{thinmathspace}{0ex}}700=\left(40\mathrm{%}-1\mathrm{%}\right)\phantom{\rule{thinmathspace}{0ex}}\text{of}\phantom{\rule{thinmathspace}{0ex}}\\ & 700=\left(280-7\right)=273\end{array}$

9.Find the principal if the interest compounded at the rate of 10% per annum for two years is Rs. 420.

Explanation:

Solution:
$\begin{array}{rl}& \text{Given},\\ & \text{Compound}\phantom{\rule{thinmathspace}{0ex}}\text{rate},\phantom{\rule{thinmathspace}{0ex}}R=10\mathrm{%}\phantom{\rule{thinmathspace}{0ex}}\text{per}\phantom{\rule{thinmathspace}{0ex}}\text{annum}\\ & \text{Time}=2\phantom{\rule{thinmathspace}{0ex}}\text{years}\\ & CI-Rs.\phantom{\rule{thinmathspace}{0ex}}420\\ & \text{Let}\phantom{\rule{thinmathspace}{0ex}}P\phantom{\rule{thinmathspace}{0ex}}\text{be}\phantom{\rule{thinmathspace}{0ex}}\text{the}\phantom{\rule{thinmathspace}{0ex}}\text{required}\phantom{\rule{thinmathspace}{0ex}}\text{principal}\\ & A=\left(P+CI\right)\\ & \text{Amount},A=\left\{P×{\left[1+\left(\frac{R}{100}\right)\right]}^{n}\right\}\\ & \left(P+CI\right)=\left\{P×{\left[1+\frac{10}{100}\right]}^{2}\right\}\\ & \left(P+420\right)=P×{\left[\frac{11}{10}\right]}^{2}\\ & P-1.21P=-420\\ & 0.21P=420\\ & \text{Hence},P=\frac{420}{0.21}=Rs.\phantom{\rule{thinmathspace}{0ex}}2000\end{array}$

10.In what time will Rs. 3300 becomes Rs. 3399 at 6% per annum interest compounded half-yearly?

$\begin{array}{rl}& P=Rs.\phantom{\rule{thinmathspace}{0ex}}3300\\ & A=Rs.\phantom{\rule{thinmathspace}{0ex}}3399\\ & R=6\mathrm{%}\phantom{\rule{thinmathspace}{0ex}}\text{per}\phantom{\rule{thinmathspace}{0ex}}\text{annum}\\ & \text{Let}\phantom{\rule{thinmathspace}{0ex}}\text{the}\phantom{\rule{thinmathspace}{0ex}}\text{time}\phantom{\rule{thinmathspace}{0ex}}\text{be}\phantom{\rule{thinmathspace}{0ex}}\text{n}\phantom{\rule{thinmathspace}{0ex}}\text{years}\text{.}\\ & \text{Compound}\phantom{\rule{thinmathspace}{0ex}}\text{interest}\phantom{\rule{thinmathspace}{0ex}}\text{is}\phantom{\rule{thinmathspace}{0ex}}\text{taken}\phantom{\rule{thinmathspace}{0ex}}\text{half - yearly}.\\ & A=P×{\left[1+\left(\frac{R}{2}×100\right)\right]}^{2n}\\ & 3399=3300{\left(1+\frac{3}{100}\right)}^{2n}\\ & {\left(1.03\right)}^{2n}=\frac{3399}{3300}\\ & {\left(1.03\right)}^{2n}={\left(1.03\right)}^{1}\\ & Thus,\phantom{\rule{thinmathspace}{0ex}}2n=1\phantom{\rule{thinmathspace}{0ex}}year\\ & n=\frac{1}{2}\text{year}=6\phantom{\rule{thinmathspace}{0ex}}\text{months}\end{array}$