Question

2. ₹ 15000 की धनराशि पर 2 वर्ष में उपार्जित वार्षिक रूप से
संयोजित चक्रवृद्धि ब्याज तथा साधारण ब्याज का अन्तर ₹ 96 है.
इस पर ब्याज की वार्षिक दर कितनी है?​

Answer 1

$\blue{\bold{\underline{\underline{Answer:}}}}$

$\green{\tt{\therefore{Rate\%=8\%}}}$

$\orange{\bold{\underline{\underline{Step-by-step\:explanation:}}}}$

$\green{ \underline \bold{Given :}} \\ \tt: \implies Principal(p) = 15000 \: rupees \\ \\ \tt: \implies Time(t) = 2 \: years \\ \\ \tt : \implies C.I- S.I= 96 \: rupees \\ \\ \red{ \underline \bold{To \: Find :}} \\ \tt: \implies Rate\% = ?$

• According to given question :

$\bold{As \: we \: know \: that} \\ \tt: \implies S.I = \frac{p \times r \times t}{100} \\ \\ \tt: \implies S.I = \frac{15000 \times r \times 2}{100} \\ \\ \green{\tt: \implies S.I= 300 \: r} - - - - - (1) \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies A = p(1 + \frac{r}{100} )^{t} \\ \\ \tt: \implies A=p(1 + \frac{r}{100} ) ^{2} \\ \\ \bold{As \: we \: know \: that} \\ \tt: \implies C.I = A - p \\ \\ \tt: \implies C.I= p(1 + \frac{r}{100} )^{2} - p - - - - - (2) \\ \\ \bold{difference : } \\ \tt: \implies C.I- S.I = 96 \\ \\ \tt: \implies p(1 + \frac{r}{100} )^{2} - p - 300r = 96 \\ \\ \tt: \implies 15000( \frac{100 + r}{100} )^{2} - 15000 - 300r = 96 \\ \\ \tt: \implies 1.5(100 + r)^{2} - 15000 - 300r = 96 \\ \\ \tt: \implies 1.5(10000 + {r}^{2} + 200r) - 15000 - 300r = 96 \\ \\ \tt: \implies 15000 + 1.5 {r}^{2} + 300r - 15000 - 300r = 96 \\ \\ \tt: \implies 1.5 {r}^{2} = 96 \\ \\ \tt: \implies {r}^{2} = \frac{96}{1.5} \\ \\ \tt: \implies {r} = \sqrt{64} \\ \\ \green{\tt: \implies r = 8 \%}$