Question

The difference between C.I. and S.I. accrued on an amount of Rs. 20,000 in 2 years was Rs. 392. Find the rate of interest per annum. *

Answer 1

ɢɪᴠᴇɴ :-

• Difference(D) between CI and SI (CI - SI ) = 392 ₹

• Principal (P) = 20,000 ₹

• Time (T) = 2 years

ᴛᴏ ғɪɴᴅ :-

• Rate (R)

Sᴏʟᴜᴛɪᴏɴ :-

We know that,

$Difference(D) = P \times ({ \frac{R}{100}) }^{n}$

Here,

➦ D = ( CI - SI)

➦ P = Principal

➦ R = Rate

➦ n = Number of years

Put the above given values in this formula, we get,

$\implies \: 392 = 20000 \times { \frac{R}{100} }^{2} \\ \\ \implies \: 392 = 20000 \times \frac{ {R}^{2} }{10000} \\ \\ \implies \: 392 = \frac{20000 \times {R}^{2} }{10000} \\ \\ \implies \: 392 = 2 {R}^{2} \\ \\ \implies \: {R}^{2} = \frac{392}{2} \\ \\ \implies \: {R}^{2} = 196 \\ \\ \implies \: R \: = \sqrt{196} \\ \\ \implies \: R = 14$

Hence,

• Rate (R) = 14 %