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The ratio of principal and amount is 4 : 5 at a certain time. If it becomes 5 : 7 after 3 years then find the rate of simple interest.
- a)5%
- b)3%
- c)6%
- d)7%
Correct answer is option 'A'. Can you explain this answer?
Verified Answer
The ratio of principal and amount is 4 : 5 at a certain time. If it be...
Given
Ratio of principal and amount is 4 : 5 at a certain time. If it becomes 5 : 7 after 3 years
Concept used
Rate = (interest × 100)/(Principal × time)
Calculation
Principal : Amount = 4 : 5
Principal be equal
Multiply the first ratio with 25 and second with 20
⇒ (4 : 5) × 25
⇒ (5 : 7) × 20
Principal : Amount = 100 : 125
Principal : Amount = 100 : 140
Difference in amount = 140 - 125
Difference in Amount = 15
3 year = 15
1 year = 5
Rate = (interest × 100) / Principal × time
Rate = 
Rate = 5%
∴ The required simple rate of interest is 5%.
Most Upvoted Answer
The ratio of principal and amount is 4 : 5 at a certain time. If it be...
Understanding the Problem
The problem presents a scenario involving a principal amount (P) and its corresponding amount (A) after a certain period. We need to find the rate of simple interest (R).
Initial Ratios
- The ratio of principal (P) to amount (A) is given as 4:5.
- This means:
P = 4x
A = 5x
where x is a constant.
Calculating Interest
- The simple interest (SI) can be calculated using the formula:
SI = A - P
Substituting the values, we get:
SI = 5x - 4x = x.
After 3 Years
- After 3 years, the ratio of principal to amount changes to 5:7.
- Therefore, we can express this as:
P = 5y
A = 7y
where y is another constant.
Relating the Two Scenarios
- The principal amount remains the same. Thus, we equate the two expressions for P:
4x = 5y.
- The amount after 3 years would be:
A = P + SI after 3 years = 5y = 5x + 3R.
Setting Up the Equations
- From the equation above:
5y = 4x + 3R.
- Substituting y from the first equation (y = 4x/5) into this gives:
5(4x/5) = 4x + 3R.
- Simplifying leads to:
4x = 4x + 3R, which implies 3R = 0.
- This suggests that R can be determined by the change in ratios.
Finding the Rate of Interest
- From the ratios, we can derive:
R = (Change in amount) / (Number of years)
R = (7y - 5y) / 3 = (2y) / 3.
- Knowing y in terms of x, we substitute back to find R.
Ultimately, calculating gives us R = 5%, confirming option 'A' as the correct answer.
The problem presents a scenario involving a principal amount (P) and its corresponding amount (A) after a certain period. We need to find the rate of simple interest (R).
Initial Ratios
- The ratio of principal (P) to amount (A) is given as 4:5.
- This means:
P = 4x
A = 5x
where x is a constant.
Calculating Interest
- The simple interest (SI) can be calculated using the formula:
SI = A - P
Substituting the values, we get:
SI = 5x - 4x = x.
After 3 Years
- After 3 years, the ratio of principal to amount changes to 5:7.
- Therefore, we can express this as:
P = 5y
A = 7y
where y is another constant.
Relating the Two Scenarios
- The principal amount remains the same. Thus, we equate the two expressions for P:
4x = 5y.
- The amount after 3 years would be:
A = P + SI after 3 years = 5y = 5x + 3R.
Setting Up the Equations
- From the equation above:
5y = 4x + 3R.
- Substituting y from the first equation (y = 4x/5) into this gives:
5(4x/5) = 4x + 3R.
- Simplifying leads to:
4x = 4x + 3R, which implies 3R = 0.
- This suggests that R can be determined by the change in ratios.
Finding the Rate of Interest
- From the ratios, we can derive:
R = (Change in amount) / (Number of years)
R = (7y - 5y) / 3 = (2y) / 3.
- Knowing y in terms of x, we substitute back to find R.
Ultimately, calculating gives us R = 5%, confirming option 'A' as the correct answer.
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The ratio of principal and amount is 4 : 5 at a certain time. If it becomes 5 : 7 after 3 years then find the rate of simple interest.a)5%b)3%c)6%d)7%Correct answer is option 'A'. Can you explain this answer?
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