Question

. A certain amount of money amounts to ₹5500 in 2 years and to ₹5750 in three years. Find the principal and rate of interest ​

Answer 1

Question:-

A certain amount of money amounts to ₹5,500 in 2 years and to ₹5,750 in three years. Find the principal and rate of interest.

Given:-

• A certain amount of money amounts to ₹5,500 in 2 years and to ₹5,750 in three years.

To Find:-

• The principal and rate of interest.

Solution:-

Let,

• Principal = (P).
• Rate of interest = (R).

$\sf \large Interest = I = \frac{ P \times \: T \times R}{100}$

$\sf \large Total \: amount (P + I) - \bigg[P + \frac{P \times T \times R }{100} \bigg]in \: 2 \: years.$

$\sf \large So,P + \frac{P \times 2 \times R }{100} = 5,500 \\ \\ \sf \large P \bigg[1 + \frac{2R}{100} \bigg] = 5,500 \: \: \: ...(i)$

In 3 years Total amount.

$\sf \large (P + I) = P + \frac{P \times 3 \times R }{100} = P \bigg(1 + \frac{3R}{100} \bigg) \\ \\ \sf \large So,P \bigg( 1 + \frac{3R}{100} \bigg) = 5,750 \: \: \: ...(ii)$

$\sf \large (i) \div (ii) \: \frac{P \bigg(1 + \frac{2R}{100} \bigg)}{P \bigg(1 + \frac{3R}{100} \bigg)} = \frac{5,500 }{5,750} \\ \\ \sf \large \frac{100 + 2R}{100 + 3R} = \frac{550}{570} \\ \\ \sf \large575(100 + 2R) = 550(100 + 3R) \\ \\ \sf \large1,150R - 1,650 = 55,000 - 57,500 \\ \\ \sf \large500R = 2,500 \\ \\ \sf \large R = \frac{2,500}{500} = 5$

${ \boxed{ \sf \large \color{red} \therefore Rate \: of \: interest = 5 \%.}}$

$\sf \large From(i) \: \: P \bigg(1 + \frac{2R}{100} \bigg) = 5,500 \\ \\ \sf \large P \bigg(1 + \frac{2 \times 5}{100} \bigg) = 5,500 \\ \\ \sf \large P \times \frac{110}{100} = 5,500 \\ \\ \sf \large P = 5,500 \times \frac{110}{100} = 5,000$

${ \boxed{ \sf \large \color{red} \therefore Principal = ₹5,000.}}$

Answer:-

● ∴ Principal = ₹5,000.

● ∴ Rate of interest = 5%.

Hope you have satisfied. ⚘

Answer 2

The Answer is in Attachment

Hope it Help you