Question

Write the proper numbers in the blanks in the table below.

Principal (Rs)	Period (years)	Rate (p.c.p.a)	Simple Interest (Rs)
500	7	6	........
.......	8	9	8640
9000	.......	5	2475
11000	6	.......	2640

Answer 1

(1) Principal (P) = Rs 500
Time (N) = 7 years
Rate (R) = 6 p.c.p.a.
We have $\mathrm{I}=\frac{\mathrm{P}\times \mathrm{R}\times \mathrm{N}}{100}$
$$\begin{gathered} \Rightarrow \mathrm{I}=\frac{500\times 6\times 7}{100} \\ \Rightarrow \mathrm{I}=5\times 6\times 7 \\ \Rightarrow \mathrm{I}=\mathrm{Rs}210 \end{gathered}$$

(2) Time (N) = 8 years
Rate (R) = 9 p.c.p.a
Interest = I = Rs 8640
We have $\mathrm{I}=\frac{\mathrm{P}\times \mathrm{R}\times \mathrm{N}}{100}$
$$\begin{gathered} \Rightarrow 8640=\frac{\mathrm{P}\times 9\times 8}{100} \\ \Rightarrow 8640=\frac{\mathrm{P}\times 72}{100} \end{gathered}$$

On multiplying both the sides by 100, we obtain:
$$\begin{gathered} 8640\times 100=\frac{\mathrm{P}\times 72}{100}\times 100 \\ \Rightarrow 864000=\mathrm{P}\times 72 \end{gathered}$$
On dividing both the sides by 72, we obtain:
$$\begin{gathered} \frac{86400}{72}=\frac{\mathrm{P}\times 42}{72} \\ \Rightarrow \mathrm{Rs}12000=\mathrm{P} \\ \mathrm{Therefore},\mathrm{Principal}=\mathrm{Rs}12000 \end{gathered}$$

(3) Principal (P) = Rs 9000
Rate (R) = 5 p.c.p.a.
Interest = I = Rs 2475
We have $\mathrm{I}=\frac{\mathrm{P}\times \mathrm{R}\times \mathrm{N}}{100}$
$$\begin{gathered} \Rightarrow 2475=\frac{9000\times 5\times \mathrm{N}}{100} \\ \Rightarrow 2475=90\times 5\times \mathrm{N} \end{gathered}$$

On dividing both the sides by 5, we obtain:
$$\begin{gathered} \frac{2475}{5}=\frac{90\times 5\times \mathrm{N}}{5} \\ \Rightarrow 495=90\times \mathrm{N} \end{gathered}$$
On dividing both the sides by 90, we obtain:
$$\begin{gathered} \frac{495}{90}=\frac{90\times \mathrm{N}}{90} \\ \Rightarrow 5.5\mathrm{year}=\mathrm{N} \end{gathered}$$
Therefore, Time = 5.5 years

(4) Principal (P) = Rs 11000
Time (N) = 6 years
Interest = I = Rs 2640
We have $\mathrm{I}=\frac{\mathrm{P}\times \mathrm{R}\times \mathrm{N}}{100}$
$$\begin{gathered} \Rightarrow 2640=\frac{11000\times \mathrm{R}\times 6}{100} \\ \Rightarrow 2640=110\times \mathrm{R}\times 6 \end{gathered}$$

On dividing both the sides by 110, we obtain:
$$\begin{gathered} \frac{2640}{110}=\frac{110\times \mathrm{R}\times 6}{110} \\ \Rightarrow 24=\mathrm{R}\times 6 \end{gathered}$$
On dividing both the sides by 6, we obtain:
$$\begin{gathered} \frac{24}{6}=\frac{\mathrm{R}\times 6}{6} \\ \Rightarrow 4\%=\mathrm{R} \\ \mathrm{Therefore},\mathrm{rate}=4\% \end{gathered}$$

Principal (Rs)	Period (years)	Rate (p.c.p.a)	Simple Interest (Rs)
500	7	6	210
12000	8	9	8640
9000	5.5	5	2475
11000	6	4	2640