Question

The difference between compound interest and simple interest at 5% per annum in 2 years is 30. Find the sum.​

Answer 1

Given :

R = 5%

T = 2 years

CI - SI = Rs 30

To find :

P = ?

Solution :

SI = P x R x T/100

SI = P x 5 x 2/100

SI = P/10

And

A = P(1 + 5/100)²

A = P(21/20)²

A = 441 P/400

CI = A - P

=> 441 P/400 - p

=> 441 P - 400 P/400

=> 41 P/400

=> CI - SI = Rs 30

=> 41 P/400 - p/100 = 30

=> 41 P - 40 P = 30

=> P/100 = 30

=> P = 400 x 30

=> Rs 12000

∴ Sum is 12000

Answer 2

Answer:

• Rate = 5% per annum
• Time = 2 years.
• Sum = ?

• Difference b/w CI & SI for 2 years :

$:\implies\sf Difference=\dfrac{Principal \times (Rate)^2}{100^2}\\\\\\:\implies\sf 30=\dfrac{Principal \times (5)^2}{100^2}\\\\\\:\implies\sf 30=\dfrac{Principal \times 5 \times 5}{100 \times 100}\\\\\\:\implies\sf 30=\dfrac{Principal }{20 \times 20}\\\\\\:\implies\sf 30 \times 20 \times 20 = Principal\\\\\\:\implies\underline{\boxed{\sf Principal = Rs. \:12000}}$

⠀

$\therefore\:\underline{\textsf{Hence, the sum is \textbf{Rs. 12,000}}}.$