a certain sum of money amounts to rupees 6300 in 2 years and 7875 in 3 years 9 months at simple interest the rate of interest per annum is
Answers
Answer:
Let P be the initial sum and r be the annual rate of interest,
Since, the amount formula in simple interest,
A=P+\frac{P\times r\times t}{100}A=P+
100
P×r×t
Where,
t = number of years,
Here, if t = 2 years then A = 6300,
\implies 6300 = P+\frac{P\times r\times 2}{100}=P+\frac{Pr}{50}⟹6300=P+
100
P×r×2
=P+
50
Pr
\implies P(1+\frac{r}{50}) = 6300\implies P = \frac{6300}{1+\frac{r}{50}}⟹P(1+
50
r
)=6300⟹P=
1+
50
r
6300
If t = 3 years 9 months = 3\frac{3}{4}3
4
3
years then A = 7875,
\implies 7875 = P + \frac{P\times r\times 3\frac{3}{4}}{100}=P+\frac{P\times r\times \frac{15}{4}}{100}=P(1+\frac{3r}{80})⟹7875=P+
100
P×r×3
4
3
=P+
100
P×r×
4
15
=P(1+
80
3r
)
By substituting the value of P,
7875 = \frac{6300}{1+\frac{r}{50}}((1+\frac{3r}{80})7875=
1+
50
r
6300
((1+
80
3r
)
7875(1+\frac{r}{50}) = 6300 + \frac{18900r}{80}7875(1+
50
r
)=6300+
80
18900r
7875+157.5r= 6300 + 236.25r7875+157.5r=6300+236.25r
7875 - 6300 = 236.25r - 157.5r7875−6300=236.25r−157.5r
1575 = 60.75r1575=60.75r
\implies r = \frac{1575}{60.75}=25.93\%⟹r=
60.75
1575
=25.93%