Question

At what per cent per annum simple interest Rs 650 will amount to Rs 741 in 3 year and 6 month ?​

Answer 1

$\huge\mathcal{\fcolorbox{cyan}{black}{\pink{Answer࿐}}}$

★The rate of interest is 4%.

Step-by-step explanation:

Principal = Rs. 650

Amount = Rs. 741

Time = years and 6 months = 3.5 years

Using the given information we get

$interest \: = amount - principal = 741 - 650 = 91$

Formula of simple interest:

$I = \frac{P \times R \times T}{100}$

where, P is principal, r is rate of interest, t is time in years.

$91 = \frac{651 \times r \times 3.5}{100}$

$91 = 22.75 \times r$

$r \: = 91 \div 22.75$

$r = 4$

★Therefore, the rate of interest is 4%.

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Answer 2

Answer:

Given:-

At what percent per annum simple interest ₹650 will amount to ₹741 in 3 years and 6 months?

To Find:-

Rate of interest ( percent per annum ).

Note:-

●》Here at first, we will take time in year as it is asked for "per annum" which means per year; For finding rate of interest, we need to have interest amount. For calculating interest, we will use the formula for finding amount i.e. Amount = Principal - Interest.

●》For finding unknown value, known value needs to transposed from its side to another and signs are also changed or not (signs are not changed in multiple and divisional value ). For example - Positive becomes Negative.

Formula Used:-

■》Rate of interest = $\dfrac{Interest × 100}{Principal × Time}$

Solution:-

[ Let's convert Time into single unit i.e. years ]

☆ We know that~

▪︎$1 year = \dfrac{1}{12} years$

▪︎$3 years \ \ 6 months = 3 + \dfrac{6}{12} years$

▪︎$3 years \ \ 6 months = 3 + \dfrac{1}{2} years$

▪︎$3 years \ \ 6 months = \dfrac{6}{2} + \dfrac{1}{2} years$

▪︎$3 years \ \ 6 months = \dfrac{7}{2} years$

▪︎$3 years \ \ 6 months = 3 \ \dfrac{1}{2} years$

$\huge\pink{Time = 3 \ \dfrac{1}{2} years}$

_______________________________

[ Now , interest ]

$\huge\red{Amount = ₹741, Principal = ₹650}$

$\huge\red{\ \ \ \ Interest = ?, Let \ \ it \ \ be \ \ "x"}$

☆ According to note first point~

▪︎$Amount = Principal + Interest$

▪︎$₹741 = ₹650 + x$

☆ According to note second point ( transposing )~

▪︎$₹741 - ₹650 = x$

▪︎$₹91 = x$

$\huge\pink{Interest = x => ₹91}$

_______________________________

[ Now, Rate of interest ]

$\huge\red{Interest = ₹91, Principal = ₹650, Time = 3 \ \dfrac{1}{2} years}$

$\huge\red{\ \ \ \ Rate \ \ of \ \ interest = ?}$

☆ According to Formula Used~

▪︎$Rate \ \ of \ \ Interest = \dfrac{Interest × 100}{Principal × Time}$

▪︎$Rate \ \ of \ \ interest = \dfrac{91 × 100}{650 × 3 \ \frac{1}{2}}$

▪︎$Rate \ \ of \ \ interest = \dfrac{9,100}{650 × \frac{7}{2}}$

▪︎$Rate \ \ of \ \ interest = \dfrac{9,100}{325 × 7}$

▪︎$Rate \ \ of \ \ interest = \dfrac{9,100}{2,275}$

☆ After division~

▪︎$Rate \ \ of \ \ interest = 4$

☆ Percent Per annum~

▪︎$Rate \ \ of \ \ interest = 4$ % $\ \ per \ \ annum$

$\huge\green{Rate \ \ of \ \ interest = 4}$ % $\huge\green{\ \ per \ \ annum}$

Answer:-

Hence, the rate of interest = 4% per annum.

:)