A sum was invested at simple interest at a certain interest for 2 years. It would have fetched Rs. 60 more had it been invested at 2% higher rate. What was the sum?
A. Rs. 1500
B. Rs. 1300
C. Rs. 2500
D. Rs. 1000
Answer: Option A
Solution(By Examveda Team)
Let the rate be R at which Principal P is invested for 2 years.According to question,
{Interest at Rate (R + 2)}% - (interest at rate R%) = Rs. 60
$$\frac{{\left( {P \times 2 \times \left( {R + 2} \right)} \right)}}{{100}} - $$ $$\frac{{\left( {P \times 2 \times R} \right)}}{{100}}$$ $$ = 60$$
$$\eqalign{ & \frac{{ {2PR + 4P - 2PR} }}{{100}} = 60 \cr & 4P = 60 \times 100 \cr & {\text{Or}},P = \frac{{60 \times 100}}{4} \cr & {\text{Hence}},P = {\text{Rs}}{\text{.}}\,1500 \cr} $$
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It would have fetched Rs. 60 more had it been invested at 2% higher rate. So,
2% = 60 Rs;
100% = 3000 Rs. ( for 2 years )
1500 Rs for 1 years.
Simply , we can write , for 2 years,
2*2% = 4% ==60 Rs.
So, 100% == 1500 Rs.