Question

If Sohail pays ₹ 1.30 for using Prabhu’s money from 2nd January to 7th January at 3% per month, how much loan had Sohail taken from Prabhu?

Answer 1

Hint: Amount = ₹ 1.30, N= 6 days, R= $\dfrac{3}{{365}}\% $, let principal amount be x.
While calculating simple interest by days, use the number of days for N and divide the interest rate by 365.
Also, Amount (A) = Principal amount (P) + Simple Interest (S.I) and Simple Interest = $\dfrac{{P \times N \times R}}{{100}}$

Complete step-by-step answer:
We will first calculate simple interest
$\therefore S.I = \dfrac{{x \times 6 \times \dfrac{3}{{365}}}}{{100}}$
$ = \dfrac{{x \times 6 \times 3}}{{100 \times 365}}$
Now we will Multiply the product of 6 & 3 and 365 & 100
$\therefore S.I = \dfrac{{18x}}{{36500}}$

Now we will find the quotient of 10 & 36500 to find S.I
$\therefore S.I = 0.00049x$ …… (1)
Now we will substitute the value of S.I from equation 1 in the formula of Amount
$\therefore 1.30 = x + 0.00049x$
Now we will add the coefficient of x
$
  \therefore 1.30 = 1.00049x \\
    \\
 $
Now we will find the quotient of 1.30 & 1.00049 to find x which is the principal amount
$x = \dfrac{{1.30}}{{1.00049}}$
$\therefore x = 1.2994$
Hence, Sohail has taken a loan amount of ₹ 1.2994 from Prabhu.

Note: Avoid understanding the amount ₹ 1.30 as the principal amount. The principal amount and amount are different.