Simple Interest Ratio Calculation
The problem requires finding the ratio $x : y$ based on equal simple interest yields from two different investments.
Understanding Simple Interest
The formula for Simple Interest (SI) is:
$ SI = \frac{P \times R \times T}{100} $
Where:
- $P$ is the Principal amount
- $R$ is the Rate of interest per annum
- $T$ is the Time period in years
Calculating Interest Yields
Interest from investment ₹$x$:
- Principal ($P_x$) = $x$
- Rate ($R_x$) = 9%
- Time ($T_x$) = 5 years
- Interest ($SI_x$) = $ \frac{x \times 9 \times 5}{100} = \frac{45x}{100} $
Interest from investment ₹$y$:
- Principal ($P_y$) = $y$
- Rate ($R_y$) = 6.25%
- Time ($T_y$) = 8 years
- Interest ($SI_y$) = $ \frac{y \times 6.25 \times 8}{100} = \frac{50y}{100} $
Equating the Interests
The problem states that the interests are the same:
$ SI_x = SI_y $
$ \frac{45x}{100} = \frac{50y}{100} $
Finding the Ratio $x : y$
We can simplify the equation by cancelling out the denominator $100$:
$ 45x = 50y $
To find the ratio $x : y$, we rearrange the equation:
$ \frac{x}{y} = \frac{50}{45} $
Now, simplify the fraction:
$ \frac{x}{y} = \frac{50 \div 5}{45 \div 5} = \frac{10}{9} $
Therefore, the ratio $x : y$ is $10 : 9$.
Similar Questions
- A sum of ₹ 2,000, invested at the rate of 8.5% simple interest per annum for 6 years will yield an interest of:
Important Questions from Simple Interest
If ₹12,800 is invested in a bank for 5 years at the rate of 9% per annum simple interest. what amount is returned by the bank?
Somu has borrowed ₹10,000 from a money lender with simple interest at a rate of 7% half yearly. How much amount will he pay to the money lender after 3 years?
Find the Simple interest on Rs. 2,400 from 20 March 2019 to 31 may 2019 at \(6{1 \over 4}\) % rate?
If the simple interest for five years is equal is 35% of the principal, that rate of interest is:
A sum fetched a simple interest of Rs. 3,040 at the rate of 8% p.a in 5 years. what is the sum?
