Question
10. What rate gives \( ₹ 280 \) as interest on a sum of \( ₹ 56,000 \) in 2 years? 11. If Meena gives an interest of \( ₹ 45 \) for one year at \( 9 \% \) rate p.a.. What is the sung has borrowed?
Ask by Christensen Chadwick. in the United Arab Emirates
Feb 18,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The rate that gives ₹280 as interest on a sum of ₹56,000 in 2 years is 0.25% per annum. Meena has borrowed ₹500.
Solution
To find the rate that gives ₹280 as interest on a sum of ₹56,000 in 2 years, we can use the formula for simple interest:
\[ \text{Simple Interest} = \frac{P \times R \times T}{100} \]
where:
- \( P \) is the principal amount (₹56,000),
- \( R \) is the rate of interest (to be found),
- \( T \) is the time period (2 years),
- \( I \) is the interest (₹280).
Given that the interest is ₹280, we can rearrange the formula to solve for the rate of interest:
\[ R = \frac{100 \times I}{P \times T} \]
Substitute the given values:
- \( I = 280 \),
- \( P = 56000 \),
- \( T = 2 \).
\[ R = \frac{100 \times 280}{56000 \times 2} \]
Now, let's calculate the rate of interest.
Calculate the value by following steps:
- step0: Calculate:
\(\frac{100\times 280}{\left(56000\times 2\right)}\)
- step1: Remove the parentheses:
\(\frac{100\times 280}{56000\times 2}\)
- step2: Multiply the numbers:
\(\frac{28000}{56000\times 2}\)
- step3: Multiply the numbers:
\(\frac{28000}{112000}\)
- step4: Reduce the fraction:
\(\frac{1}{4}\)
The rate of interest that gives ₹280 as interest on a sum of ₹56,000 in 2 years is 0.25% per annum.
Now, let's move on to the second part of the problem. If Meena gives an interest of ₹45 for one year at a 9% rate p.a., we need to find the sum she has borrowed. We can use the formula for simple interest again:
\[ \text{Simple Interest} = \frac{P \times R \times T}{100} \]
Given that the interest is ₹45, the rate is 9%, and the time period is 1 year, we can rearrange the formula to solve for the principal amount:
\[ P = \frac{100 \times I}{R \times T} \]
Substitute the given values:
- \( I = 45 \),
- \( R = 9 \),
- \( T = 1 \).
\[ P = \frac{100 \times 45}{9 \times 1} \]
Now, let's calculate the principal amount.
Calculate the value by following steps:
- step0: Calculate:
\(\frac{100\times 45}{\left(9\times 1\right)}\)
- step1: Remove the parentheses:
\(\frac{100\times 45}{9\times 1}\)
- step2: Multiply the numbers:
\(\frac{4500}{9\times 1}\)
- step3: Rewrite the expression:
\(\frac{4500}{9}\)
- step4: Reduce the fraction:
\(500\)
The sum Meena has borrowed is ₹500.
Answered by UpStudy AI and reviewed by a Professional Tutor
Like
error msg
Explain 
Simplify this solution Mind Expander
To find the rate that yields ₹ 280 as interest on a sum of ₹ 56,000 in 2 years using the formula for simple interest \( I = \frac{P \times R \times T}{100} \), we can rearrange it to find R: \( R = \frac{I \times 100}{P \times T} \). Plugging in the values, \( R = \frac{280 \times 100}{56,000 \times 2} = 2.5\% \). So, the rate is 2.5% per annum. To determine how much Meena borrowed, we can use the same simple interest formula rearranged as \( P = \frac{I \times 100}{R \times T} \). Here, \( P = \frac{45 \times 100}{9 \times 1} = 500 \). Thus, the sum Meena borrowed is ₹ 500.
