Question

the difference between the simple interest and the compound interest on a sum for 3 year is ₹ 300 at the rate percent of 10% p.a find the sum​

Answer 1

Given:

Interest rate =10% per annum

Time =3 years.

We know that:

Simple interest (SI)=PTR/100

where P is principle amount, T is time taken, R is rate per annum

Let sum is P, then

SI=(P×3×10)/100

⇒SI=(30P)/100

⇒SI=(3P)/10 —————- equation 1

To find the amount we have the formula,

Amount (A)=P(1+(r/100))

n

where P is present value, r is rate of interest, n is time in years.

Also CI=A−P

Now substituting the values in above formula we get,

∴CI=P(1+10/100)

3

−P

⇒CI=P(1+1/10)

3

−P

⇒CI=P(11/10)

3

−P

⇒CI=P(1331)/(1000)–P

⇒CI=331P/1000 ——– equation 2

Now the difference is

(CI–SI)=331P/1000–(3P)/10

$$\RIghtarrow 93 = 331P- 300P/1000$$

⇒93=31P/1000

⇒P=93×1000/31

⇒P=3×1000

⇒P=3000

∴ Sum $$= ₹\3000$$