[2575] The difference between the simple interest and true discount on a certain sum of money for 6 months

For Competitive Exams

The difference between the simple interest and true discount on a certain sum of money for 6 months at 6% per annum is Rs. 2.25 . Find the sum?

7525

2255

2575

2755

Explanation:

Given that,
Time = 6 months =$\dfrac{1}{2}$ of year
Rate =6%
Consider,
True discount = $\dfrac{A∗R∗T}{100+(R∗T)}$
=>True discount = $\dfrac{x∗6∗\dfrac{1}{2}}{100+(6∗\dfrac{1}{2})}$
=>True discount =x*$(\dfrac{6}{2})*(\dfrac{2}{206})$
=>True discount =$\dfrac{6x}{206}$
=>True discount =$\dfrac{3x}{103}$
Now,
S.I = (Amount * R * T) / 100 Simple interest =(x*6 * $\dfrac{1}{2} \times \dfrac{1}{100}$)
=> Simple interest=$\dfrac{3x}{100}$
Therefore,
$\dfrac{3x}{100}$ –$\dfrac{3x}{103}$ = 2.25
⇒ (103*3x) – (100*3x) = 2.25 * 100 * 103
⇒ x =2575
Therefore, sum due = Rs. 2575.

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