With a given rate of simple interest,the rati | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) Let the principal be $P$ and the rate of interest be $R \%$ per annum.For the first period $t$,the ratio of principal to amount is $P : (P + SI_t)

Vedclass · Accepted Answer

$5$

Vedclass · Answer

(B) Let the principal be $P$ and the rate of interest be $R \%$ per annum.For the first period $t$,the ratio of principal to amount is $P : (P + SI_t) = 4 : 5$.This implies $P + SI_t = \frac{5}{4}P$,so $SI_t = \frac{1}{4}P$.Using $SI = \frac{P 	imes R 	imes t}{100}$,we have $\frac{P 	imes R 	imes t}{100} = \frac{1}{4}P$,which gives $Rt = 25$.After $3$ years,the time becomes $t + 3$. The ratio of principal to amount is $P : (P + SI_{t+3}) = 5 : 7$.This implies $P + SI_{t+3} = \frac{7}{5}P$,so $SI_{t+3} = \frac{2}{5}P$.Using the formula again,$\frac{P 	imes R 	imes (t+3)}{100} = \frac{2}{5}P$,which gives $R(t+3) = 40$.Expanding this,$Rt + 3R = 40$.Substituting $Rt = 25$,we get $25 + 3R = 40$.$3R = 15$,so $R = 5$.The rate of interest is $5 \%$ per annum.

With a given rate of simple interest,the ratio of principal and amount for a certain period of time is $4:5$. After $3$ years,with the same rate of interest,the ratio of the principal and amount becomes $5:7$. The rate of interest per annum is (in $\%$):

Similar Questions

The annual instalment that will discharge a debt of ₹ $4200$ due in $5$ years at $10 \%$ simple interest (in ₹) is:

Simple interest received by a person in $10$ $years$ on a principal of ₹ $9500$ is $130 \%$ of the principal. What is the rate of interest (in $\%$) per annum?

Divide ₹ $2379$ into $3$ parts so that their amounts after $2, 3$ and $4$ years respectively may be equal,the rate of interest being $5 \%$ per annum at simple interest. The first part is (in ₹):

$A$ sum of $Rs. 1500$ amounts to $Rs. 3000$ in five years at a certain rate of simple interest. If the rate of interest is increased by $1 \%$,the same sum in the same time would amount (in $Rs.$) to:

The population of a city increases at the rate of $5 \%$ $p.a.$ If the present population of the city is $370440$,then what was its population (in $lakh$) $3$ years ago?

Vedclass Test Series

Exam Paper Generator

Online Exam Module