1.

A sum was put at simple interest at a certain rate for 3 years. Had it been put at 3% higher rate, it would have fetched Rs. 27 more. The sum is?1). Rs. 4002). Rs. 2503). Rs. 3004). Rs. 500

Answer»

Formula for Simple Interest -

$(SI = \FRAC{{P \times R \times T}}{{100}})$

Where,

P = Principal

R = RATE of interest

T = Time period

Let the sum be Rs. x and the original rate be R%,

Then, $({\RM{SI}} = \frac{{{\rm{X}} \times {\rm{\;R}} \times {\rm{}}3}}{{100}})$

When rate is increased by 3%

Then, R = R + 3

And $(SI = \frac{{{\rm{X}} \times {\rm{}}\left( {{\rm{R}} + 3} \RIGHT){\rm{}} \times {\rm{}}3}}{{100}})$

According to the question, the difference between the two EQUATIONS is Rs. 27

$(\therefore \frac{{{\rm{X}} \times {\rm{}}\left( {{\rm{R}} + 3} \right){\rm{}} \times {\rm{\;}}3}}{{100}}{\rm{}} - {\rm{}}\frac{{{\rm{X}} \times {\rm{\;R}} \times {\rm{}}3}}{{100}} = 27)$

$(\Rightarrow \frac{{3{\rm{XR}} + 9{\rm{X}} - 3{\rm{XR}}}}{{100}} = 27)$

$(\Rightarrow \frac{{9{\rm{X}}}}{{100}} = 27)$

⇒ 9X = 2700

⇒ X = 2700/9

⇒ X = 300

∴ The sum is of Rs. 300.


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