Solution

\[ \begin{align*} \color{green} \text{Simple Interest} & = \color{green} \frac{P \times R \times T}{100} \\ \\ & = \frac{\cancel{100}^{4} \times 5 \times 3}{\cancel{100}^{1}} \\ \\ & = 4 \times 5 \times 3 \\ S.I & = \text{₹} 60 \\ \\ \color{green} A & = \color{green} P + S.I \\ & = 400 + 60 \\ A & = \text{₹}460 \end{align*} \]

Answer \( S.I = {\color{red}\text{₹} 60} , Amount = {\color{red}\text{₹} 460} \)

Solution

\[ \begin{align*} P & = \text{₹}450 \\ \\ R & = 4\frac{1}{2} \% \implies \frac{9}{2} \% \\ \\ T & = 3 \, years + 4 \, months \\ & = 3 + \frac{\cancel{4}^{1}}{\cancel{12}^{3}} \\ \\ & = 3 + \frac{1}{3} \\ \\ T & = \frac{10}{3} \, years \\ \\ \color{green} S.I & = \color{green} \frac{P \times R \times T}{100} \\ \\ & = \frac{ \cancel{450}^{\color{green}45} \times \cancel{9}^{3} \times \cancel{10}^{\color{red}1}}{2 \times \cancel{3}^{1} \times {{\cancel{100}_{\cancel{\color{red}10}}}}_{\color{green}1} } \\ \\& = \frac{45 \times 3}{2} \\ \\ & = \frac{135}{2} \\ \\ S.I & = \text{₹} 67.50 \\ \\ \color{green} A & = \color{green} P + S.I \\ & = 450 + 67.50 \\ A & = \text{₹} 517.50 \end{align*} \]

Answer \( S.I = {\color{red}\text{₹} 67.50} , Amount = {\color{red}\text{₹} 517.50} \)

Solution

\[ \begin{align*} P & = \text{₹}500 \\ \\ R & = 15\frac{1}{2} \% \implies \frac{31}{2} \% \\ \\ T & = \frac{146}{365} \text{ years} = \frac{2}{5} \text{ years} \\ \\ \color{green} S.I & = \color{green} \frac{P \times R \times T}{100} \\ \\ & = \frac{{{\cancel{500}^{\cancel{\color{red}5}}}}^{\color{green}1} \times 31 \times \cancel{2}^{\color{orange}1}}{\cancel{2}_{\color{orange}1} \times \cancel{100}_{\color{red}1} \times \cancel{5}_{\color{green}1}} \\ \\ S.I & = \text{₹} 31 \\ \\ \color{green} A & = \color{green} P + S.I \\ & = 500 + 31 \\ A & = \text{₹} 531 \end{align*} \]

Answer \( S.I = {\color{red}\text{₹} 31} , Amount = {\color{red}\text{₹} 531} \)

Solution

\[ \begin{align*} P & = \text{₹}1200 \\ R & = 15\% \\ \text{Time Period} & \implies 8 \text{ April to 20 June} \\ April& = 22 \, days \\ May & = 31 \, days \\ June & = 20 \, days \\ Total \, \, days& = 73 \text{ days} \\ \\ T & = \frac{73}{365} \text{ years} \implies \frac{1}{5} \text{ years} \\ \\ \color{green} S.I & = \color{green} \frac{P \times R \times T}{100} \\ \\ & = \frac{\cancel{1200}^{\color{green}12} \times \cancel{15}^{\color{red}3} \times 1}{\cancel{100}_{\color{green}1} \times \cancel{5}_{\color{red}1}} \\ \\ & = 12 \times 3 \\ S.I & = \text{₹} 36 \\ \\ \color{green} A & = \color{green} P + S.I \\ & = 1200 + 36 \\ A & = \text{₹} 1236 \end{align*} \]

Answer \( S.I = {\color{red}\text{₹} 36} , Amount = {\color{red}\text{₹} 1236} \)

Solution

\[ \begin{align*} P & = \text{₹} 4500 \\ \text{Rate} & = 5 \text{ paise per rupee} \implies 5\% \\ \text{Time} & = 2 \text{ years} \\ \\ \color{green} S.I & = \color{green} \frac{P \times R \times T}{100} \\ \\ & = \frac{\cancel{4500}^{\color{red}45} \times 5 \times 2}{\cancel{100}_{\color{red}1}} \\ \\ & = 45 \times 10 \\ S.I & = \text{₹} 450 \\ \\ \color{green} A & = \color{green} P + S.I \\ & = 4500 + 450 \\ A & = \text{₹} 4950 \end{align*} \]

Answer \( S.I = {\color{red}\text{₹} 450} , Amount = {\color{red}\text{₹} 4950} \)

Solution

\[ \begin{align*} P & = \text{₹} 80000 \\ R & = 12\% \\ T & = 7 \text{ months} \implies \frac{7}{12} \text{ years} \\ \\ \color{green} S.I & = \color{green} \frac{P \times R \times T}{100} \\ \\ & = \frac{\cancel{80000}^{\color{blue}800} \times \cancel{12}^{\color{red}1} \times 7}{\cancel{100}_{\color{blue}1} \times \cancel{12}_{\color{red}1}} \\ \\ & = 800 \times 7 \\ S.I & = \text{₹} 5600 \\ \\ \color{green} A & = \color{green} P + S.I \\ & = 80000 + 5600 \\ A & = \text{₹} 85600 \end{align*} \]

Answer \( S.I = {\color{red}\text{₹} 5600} , Amount = {\color{red}\text{₹} 85600} \)

Solution

\[ \begin{align*} & \color{orange}Rahul \\ P & = \text{₹} 7000 \\ R & = 7\% \\ T & = 4 \frac{1}{2} \text{ years} \implies \frac{9}{2} \text{ years} \\ \\ \color{green} S.I & = \color{green} \frac{P \times R \times T}{100} \\ \\ & = \frac{{{\cancel{7000}^{\cancel{\color{red}70}}}}^{\color{green}35} \times 7 \times 9}{\cancel{100}_{\color{red}1} \times \cancel{2}_{\color{green}1}} \\ \\ & = 35 \times 63 \\ S.I & = \text{₹} 2205 \\ \\ \color{green} A & = \color{green} P + S.I \\ & = 7000 + 2205 \\ \color{magenta}\text{Rahul's Amount} & = \text{₹} 9205 \\ \\& \color{orange}Rohan \\ P & = \text{₹} 7000 \\ R & = 6\% \\ T & = 5 \text{ years} \\ \\ \color{green} S.I & = \color{green} \frac{P \times R \times T}{100} \\ \\ & = \frac{\cancel{7000}^{\color{red}70} \times 6 \times 5}{\cancel{100}_{\color{red}1}} \\ \\ & = 70 \times 30 \\ S.I & = \text{₹} 2100 \\ \\ \color{green} A & = \color{green} P + S.I \\ & = 7000 + 2100 \\ \color{magenta}\text{Rohan's Amount} & = \text{₹} 9100\end{align*} \]

Answer \( \color{red}Rahul \) will get more interest.

Solution

\[ \begin{align*} P & = \text{₹} 80000 \\ R & = 6\% \\ T & = 3 \text{ years} \\ \\ \color{green} S.I & = \color{green} \frac{P \times R \times T}{100} \\ \\ & = \frac{\cancel{80000}^{\color{red}800} \times 6 \times 3}{\cancel{100}_{\color{red}1}} \\ \\ & = 800 \times 18\\ S.I & = \text{₹} 14400 \\ \\ \color{green} A & = \color{green} P + S.I \\ & = 80000 + 14400 \\ A & = \text{₹} 94400 \\ \\ \text{Amount } & = 94400 \\ \text{Cost of the car} & = 90000 \\ \text{Money left with him} & = 94400 - 90000 \\ & = \text{₹} 4400 \end{align*} \]

Answer Money left with him \( = \color{red} \text{₹} 4400 \)