Math, asked by Rahim786, 1 year ago

Mr A invests a certain sum of money for 3 years at simple rate of interest p.a. which fetches an interest on Rs 225.Mr B invests the same sum of money for 2 years at a compound rate of interest which is equal to the rate at which Mr. A invests.Mr B earns Rs 153 by way of interest.find the sum of money and the common rate of interest.

Answers

Answered by amitnrw
2

Given : Mr A invests a certain sum of money for 3 years at simple rate of interest p.a. which fetches an interest on Rs 225.

Mr B invests the same sum of money for 2 years at same rate but compounded annually and earn Rs 153 as interest

To Find :   the sum of money and the common rate of interest.

Solution:

A different Approach :

Interest Earned in 3 Years = 225  Rs

=> Interest Earned in 1 Year = 75 Rs

1st Year interest will be same in both cases

Hence interest earned in 2nd year in case of compound interest

= 153 - 75 = 78 Rs

78 = 75 + 3 Rs

3 Rs additional interest is because of interest of Rs 75 earned in 1st Year

3 = 75 * R *  1/ 100

=> R  = 4

Rate of interest = 4  %

75 = P * 4 * 1 /100

=> P = 7500/4

=> P = 1,875

sum of money  = Rs 1875

the common rate of interest = 4 % per annum

Normal Approach

Amount = P

Rate of interest = R

225 = P * R * 3 /100

=> PR = 7500

 153 = P (1 + R/100)² - P

=> 153 = P ( 1  + R²/10000 + 2R/100) - P

=> 1530000 =  10000P  + PR² + 200PR -   10000P  

=>  1530000 =  PR² + 200PR

=> 1530000 =  PR(R + 200)

=>  1530000 = 7500 (R + 200)

=> 204 =  R + 200

=> R = 4

PR = 7500

=> P (4) = 7500

=> P = 1875

sum of money  = Rs 1875

the common rate of interest = 4 % per annum

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