Question

A sum amount to 3605 rs in 219 days at 5% per annum. what will be the sum?

Answer 1

Amount = Rs.3605
Rate = 5% per annum
Time = 219 days or 219/365 (in years)
Let Principal be x
Simple Interest = PRT/100 which is x*5*219/100*365=3x/100
3x/100 + x =3605
=> 103x=360500
=> x=360500/103
Therefore Principal = Rs.3500

Answer 2

The sum is Rs. 3500

Given :

A sum amount to 3605 rs in 219 days at 5% per annum

To find :

The sum

Formula Used :

In case of Simple interest

Principal = P

Interest = I

Time = t

Rate of interest = r %

$\displaystyle \sf{}I = \frac{Prt}{100}$

Amount = P + I

Solution :

Step 1 of 2 :

Form the equation to calculate the sum

Let the sum is Rs. P

Principal = P = ?

Amount = Rs. 3605

Interest = I = Rs. (3605 - P)

Time = t = 219 days = 219/365 year = 3/5 year

Rate of interest = r % = 5%

We know that in case of simple interest

$\displaystyle \sf{}I = \frac{Prt}{100}$

$\implies \displaystyle \sf{}(3605-P)= \frac{P \times 5 \times 3}{100\times 5}$

Step 2 of 2 :

Calculate the sum

$\implies \displaystyle \sf{}(3605-P)= \frac{P \times 5 \times 3}{100\times 5}$

$\displaystyle \sf{ \implies }(3605-P)= \frac{3P }{100}$

$\displaystyle \sf{ \implies }3P = 100(3605 - P)$

$\displaystyle \sf{ \implies }3P = 360500 - 10P$

$\displaystyle \sf{ \implies }3P + 100P= 360500$

$\displaystyle \sf{ \implies }103P = 360500$

$\displaystyle \sf{ \implies }P = 3500$

Hence the required sum is Rs. 3500

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