EXERCISE:7.4
Question 1
Simple Interest $=\frac{\text { principal } \times \text { Rate } \times \text { Time }}{100}$
i.e $I=\frac{P \times R \times T}{100}$.
i) $\quad p=350 \quad ; \quad R=11 \% \quad T=2$ years
$I=\frac{350 \times 11 \times 2}{100}$
I=Rs 77
Total amount $=S \cdot I+P$
$=77+350$
=Rs 427
ii) $p=20,000 \quad T=4 \frac{1}{2}=\frac{9}{2}$ years $; R=8 \frac{1}{2}=\frac{17}{2} \%$
$\begin{aligned} I=& \frac{20,00 \times \frac{17}{2} \times \frac{9}{2}}{160} \\ &=\frac{20000 \times 17 \times 9}{4 \times 100} \\ &=₹ 7650 \end{aligned}$
∴ Amount = principal + I
=20,000+ 7,650
= 27,650
iii) $p=₹ 648 ; R=16 \frac{2}{3}=\frac{50}{3} ; T=8$ months = $\frac{8}{12}$ years
$I=\frac{648 \times \frac{50}{3} \times \frac{8}{12}}{100}$
$I=\frac{648 \times 50 \times 8}{36 \times 100}$
I=Rs 73
$\begin{aligned} \text { Amount } &=S \cdot 1+P \\ &=73+648 \\ &=₹ 721 \end{aligned}$
Question 2
i) $S \cdot I=200, \quad p=2,500, \quad R=4 \%$
$I=\frac{P \times R \times I}{100}$
Time, $T=\frac{100 \times \underline{1}}{P \times R} .$
$T=\frac{100 \times 200}{2,500 \times 4}$
$T=2$ years
ii) $S \cdot I=2730, \quad P=12,000, R=6 \frac{1}{2}=\frac{13}{2}$
$\begin{aligned} T=& \frac{100 \times I}{P \times R} \\=& \frac{100 \times 2730}{12,000 \times 13 / 2} \\ &=\frac{100 \times 2730 \times 2}{12000 \times 13} \end{aligned}$
$T=\frac{7}{2}$ years $=3 \frac{1}{2}$ years
Question 3
i) $P=1560, \quad I=585, \quad T=3$ yeass
$I=\frac{p \times R \times T}{100}$
Rate of interest R= $\frac{100 \times I}{P \times T}$
$R=\frac{100 \times 585}{1560 \times 3}=(1.25 \times 100) \%$
$R=\frac{25}{2} \%=12 \frac{1}{2} \%$
ii) $I=325, \quad p=1625, \quad T=2 \frac{1}{2}=\frac{5}{2}$ years
$\begin{aligned} R &=\frac{100 \times I}{P \times J} \\ &=\frac{100 \times 325}{1625 \times 5 / 2} \\ &=\frac{100 \times 325 \times 2}{1625 \times 5} \\ &=8 \% \end{aligned}$
Question 4
i) $R=16 \% ; T=2 \frac{1}{2}$ years $=\frac{5}{2}$ years, $I=3840$
$I=\frac{P R I}{100}$
$P=\frac{100 \times I}{R \times T}$
$P=\frac{100 \times 3840}{16 \times 5 / 2}$
$P=\frac{100 \times 3840 \times 2}{16 \times 5}$
P=Rs 9600
∴ Principal = Rs 9600
ii) $R=7 \frac{1}{2}=\frac{15}{2} \% \quad ; \quad T=2$ years 4 months $\quad I=2730$
$=\left(2+\frac{4}{12}\right)$ year
$=\left(2+\frac{1}{3}\right)$ years
$=\frac{7}{3}$ years
$\begin{aligned} P &=\frac{100 \times I}{R \times T} \\ &=\frac{100 \times 2730}{\frac{15}{2} \times \frac{7}{3}} \\ &=\frac{100 \times 2730 \times 6}{15 \times 7} \end{aligned}$
Principal p = Rs 15,600
Question 5
i) Amount = Rs 1320; Principal = Rs 1200
S.I = A-P = 1320 - 1200
S.I = 120
$I=\frac{P \times R \times I}{100}$
$R=\frac{100 \times I}{P \times T}$
$R=\frac{100 \times 120}{1200 \times 2}$
$R=5 \%$ per annum
ii) Amount=Rs 400; principal =Rs 300
$S: I=A-P=400-300$
I=Rs 100
$R=\frac{100 \times 100}{300 \times 2}$
$R=\frac{50}{3}=16 \frac{2}{3} \%$ pes annam.
Question 6
i) $A=1950, P=1250, R=16 \%$
$I=A-P=1950-1250= 700$
$I=\frac{P \times R \times T}{100}$
$T=\frac{100 \times I}{P \times R}$
$T=\frac{100 \times 700}{1250 \times 16}$
$\quad$ Time, $T=\frac{7}{2}$ years
ii) $A=8447.50, P=6540 ; R=12 \frac{1}{2}=\frac{25}{2} .$
$I=A-P=8447.5-6540$
$I=19075$
Time, $\begin{aligned} T &=\frac{100 \times 1907.5}{6540 \times 25 / 2} \\ T &=\frac{100 \times 19075 \times 2}{6540 \times 25} \end{aligned}$
Time, $T=\frac{7}{3}$ years
Question 7
$R=4 \% \quad A=16,240, \quad P=14,000$
$\begin{aligned} I=& A-P=16,240-14,000 \\ & I=2,240 . \\ \text { Time } &=\frac{100 \times I}{P \times R} \\ \text { Time } &=\frac{100 \times 2,240}{14,000 \times 4} \\ &=4 \text { years } \end{aligned}$
Question 8
$T=6$ years, Given Amount invested trebled
So A 3 $\times$ Principal
A = 3p
$\begin{aligned} I=& A-\rho=3 p-p \\ & I=2 p \\ I=& \frac{P \times R \times f}{100} \\ R &=\frac{100 \times 1}{p \times 1} \\ & R=\frac{100 \times 20}{P \times 6} \\ & R=\frac{100}{3}=33 \frac{1}{3} \% \text { pes annm } \end{aligned}$
Question 9
i) $A=4,500 ; R=20 \% T=5$ years
$I=A-P$
$I=4,500-P$
Also $I=\frac{p \times R \times {j}}{100}$
$4,500-P=\frac{P \times 20 \times 5}{100}$
$4,500-P=P$
$\begin{aligned} p+p=& 4,500 \\ 2 p=4,500 \\ \text { principal, } P=2250 \end{aligned}$
ii) $A=2420, R=4, \quad T=2 \frac{1}{2}$ yeass $=\frac{5}{2}$ years
I=A-P
I=2420-P
Also $I \cdot \frac{P \times R \times 1}{100}$
$2420-p=\frac{p \times 4 \times 5}{2 \times 100}$
$2420-R=\frac{1}{10}$
$P+\frac{p}{10}=2420$
$\frac{11P}{10}=2420$
$P=\frac{2420 \times 10}{11}$
P=2200
$\therefore$ principal, P=2,200
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