Question

A sum of money at simple interest amounts to rs.24,000 in 4 years.if the rate of interest increased by 20%,the same amounts to25,800 in the same time.the original rate of interest is

Answer 1

Answer:

Step-by-step explanation:

P + I = 24000

P+PTR/100 =24000

P +P.4.R/100 =24000............................equation 1

P +P.4.[1.2R] /100 =25800............................equation 2

Dividing equation 1 and 2 after taking P common, we get

100 +4R /[100 + 4.8R} = 40/43

On soving the equation, we get R= 15%

Answer 2

Answer:

Original rate of Interest is 25 %

Step-by-step explanation:

Given: First Amount, A1 = Rs. 24000 and time, T1 = 4 years.

           Second Amount, A2 = 25800 , Rate , R2 = 20% and T2 = 4 years

To find: First rate, R1

Let P be the Principal Amount which same in both cases.

We know that Amount = Principal + Interest

Simple interest, SI = A2 - P

SI = 25800 - P

Also,

$SI=\frac{P\times R2\times T2}{100}$

$25800-P=\frac{P\times20\times4}{100}$

$25800-P=\frac{P\times20}{25}$

$25800-P=\frac{4P}{5}$

$5(25800-P)=4P$

$129000-5P=4P$

$9P=129000$

P = Rs. 14333.33

Now,

A1 = P + SI

SI = A1 - P

SI = 24000 - 14333.33 = 9666.67

And R1 is Original Rate of interest.

$SI=\frac{P\times R1\times T1}{100}$

$9666.67=\frac{9666.67\times R1\times4}{100}$

$9666.67=\frac{38666.66\:R1}{100}$

R1 = 25 %

Therefore, Original rate of Interest is 25 %