Question

What rate gives \[Rs.280\] as interest on a sum of \[Rs.56000\]in \[2\]years?

Answer 1

Hint: Since we are given only interest, we will consider this as simple interest.
Also, we know
\[SI = \dfrac{{P \times R \times T}}{{100}}\]
Where,
SI = Simple Interest
P = Principal amount
R = rate of interest(in percentage)
T = time(in years)
In the question, we are given the Principal amount, Time and Simple Interest and we need to find the Rate of Interest. Now, since we are given the value of three variables and we need to find the value of one unknown variable, we will use the above formula and then solve it further to Find the value of The unknown variable i.e.The rate of interest.

Complete step-by-step solution:
We are given, The Principal amount \[ = P = Rs.56000\]
Time of interest \[ = T = 2years\]
And, Simple Interest \[ = SI = Rs.280\]
Let us suppose, The rate of interest \[ = R\](in percentage)
Using the formula for Simple Interest and substituting the above values , we get,
\[SI = \dfrac{{P \times R \times T}}{{100}}\]
\[\Rightarrow 280 = \dfrac{{56000 \times R \times 2}}{{100}}\]
\[\Rightarrow \dfrac{{280}}{1} = \dfrac{{56000 \times R \times 2}}{{100}}\]
\[\Rightarrow 280 \times 100 = 56000 \times R \times 2\] (Cross Multiplying)
\[\Rightarrow 28000 = 112000 \times R\]
\[\Rightarrow \dfrac{{28000}}{{112000}} = R\]
\[\Rightarrow \dfrac{1}{4} = R\]
\[\Rightarrow 0.25 = R\]
\[\therefore R = 0.25\% \]
Hence, \[0.25\% \]rate of interest will give \[Rs.280\]as interest on a sum of \[Rs.56000\]in \[2\]years.

Note: We should remember the correct formula, first of all. Then we should keep in mind that usually time is denoted in years and if the time is given in months, we need to convert the given time into years and then solve. Similarly, Rate of interest is given in percentage and we usually forget to put the percentage symbol when we have to find the rate of interest.