Question

if the difference between the CI and Si of rupees 8000 in 2 years is rupees 20 find the rate of interest if the CI is given annually​

Answer 1

✪ Question :-

if the difference between the CI and Si of rupees 8000 in 2 years is rupees 20 find the rate of interest if the CI is given annually ... ?

✰ Formula used :-

☛ Difference between CI and SI For 2 years is given by :-

P = Difference * (100/r)²

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✭ Solution :-

Given that, Principal is Rs.8000 and Difference b/w CI and SI is = Rs.20 .

Putting values in above told formula we get,

⟿ 8000 = 20 * (100/r)²

Dividing both sides by 20 ,

⟿ 400 = 100²/r²

Cross - Multiply ,

⟿ r² = 100²/400

⟿ r² = (100)² /(20)²

⟿ r² = (100/20)²

⟿ r² = (5)²

Square - root both sides now,

⟿ r = 5% .

Hence, Required Rate is 5% per annum.

Answer 2

Answer:

$\bold\red{Rate\:of\:interest}$ = $\bold{5\%}$

Step-by-step explanation:

Given:-

• Different between CI and SI = Rs.20
• Principal = Rs.8000
• Time(n) = 2 years.
• Rate of interest(r) = ?

We know principal-rate of interest formula:-

${\boxed{\bold\green{Principal = Difference \times {(\dfrac{100}{r})}^{n} }}}$

• Substituting values:-

$\hookrightarrow\sf 8000 = 20 \times {(\dfrac{100}{r})}^{2} \\\\\hookrightarrow\sf 8000 = 20 \times (\dfrac{10000}{{r}^{2} }) \\\\\hookrightarrow\sf \dfrac{10000}{{r}^{2} } =\cancel{\dfrac{8000}{20}} \\\\\hookrightarrow\sf \dfrac{10000}{{r}^{2}} = 400 \\\\\hookrightarrow\sf 400{r}^{2} = 10000 \\\\\hookrightarrow\sf {r}^{2} =\cancel{\dfrac{10000}{400}} \\\\\hookrightarrow\sf {r}^{2} = 25 \\\\\hookrightarrow\sf r =\sqrt{25} \\\\\hookrightarrow\huge{\boxed{\sf\green{r = 5\% }}}$

$\therefore\bold{\underline{Rate\:of\:interest(r) = 5\%}}$