Question

the difference between compound interest and simple interest on sum of 2 years at the same 6% interest per annum is rs 36 then that sum in ruppees is​

Answer 1

Answer:

Rs. 10,000

Step-by-step explanation:

Let the sum be Rs. P

Rate of interest ( R ) = 6 %

Time period ( T ) = 2 years

Let's find compound interest and simple interest in terms of P

We know that

Compound Interest = P{ ( 1 + R/100 )^T - 1 }

$\Rightarrow \sf CI=P\Bigg[\bigg(1+\dfrac{6}{100} \bigg)^{2} -1\Bigg]\\\\\\\Rightarrow\sf CI =P\Bigg[\bigg(\dfrac{106}{100} \bigg)^2-1\Bigg]\\\\\\\Rightarrow\sf CI =P\Bigg[\bigg(\dfrac{53}{50} \bigg)^2-1\Bigg]\\\\\\\Rightarrow\sf CI =P\Bigg(\dfrac{53^2-50^2}{50^2} \Bigg)\\\\\\\Rightarrow\sf CI =P\Bigg(\dfrac{2809-2500}{2500} \Bigg)\\\\\\\Rightarrow\sf CI =\dfrac{309P}{2500}$

We know that

Simple interest = PTR/100

⇒ SI = P × 2 × 6 / 100

⇒ SI = 12P/100

Given :

Difference between CI and SI = Rs. 36

⇒ CI - SI = Rs. 36

$\Rightarrow \sf \dfrac{309P}{2500} -\dfrac{12P}{100} =36\\\\\\\Rightarrow\sf\dfrac{309P-300P}{2500} =36\\\\\\\Rightarrow\sf\dfrac{9P}{2500} =36\\\\\\\Rightarrow\sf\dfrac{P}{2500} =4\\\\\\\Rightarrow\sf P = 4 \times 2500\\\\\\\Rightarrow \boxed{\sf P=10000}$

Another method :

Difference between CI and SI for 2 years = P( R²/100² )

Where,

• P = Principal or Sum
• R = Rate of interest

⇒ 36 = P( 6² / 100² )

⇒ 36 = 36P / 10000

⇒ 10000 = P

⇒ P = 10000

Hence the sum is Rs. 10,000.