Ratio Algebra: Simplifying the Expression
The problem asks for the value of the expression \( \frac{3m-16f}{3m+16f} \) given that the ratio \(m:f = 16:3\).
Using Ratios for Simplification
From the given ratio \(m:f = 16:3\), we can express \(m\) in terms of \(f\) or vice-versa. A common method is to assume:
- \(m = 16k\)
- \(f = 3k\)
where \(k\) is a non-zero constant.
Substituting Values into the Expression
Now, substitute these values into the expression \(\frac{3m-16f}{3m+16f}\):
- Numerator: \(3m - 16f = 3(16k) - 16(3k)\)
- Denominator: \(3m + 16f = 3(16k) + 16(3k)\)
Calculation Steps
- Calculate the numerator: \( 3(16k) - 16(3k) = 48k - 48k = 0 \)
- Calculate the denominator: \( 3(16k) + 16(3k) = 48k + 48k = 96k \)
- Form the fraction: \( \frac{0}{96k} \)
- Simplify the fraction. Since \(k \neq 0\), the value is: \( 0 \)
Therefore, the value of the expression \(\frac{3m-16f}{3m+16f}\) is 0.
Similar Questions
- An amount is divided between two friends in the ratio 4: 7. If the second part is ₹6 more than the first, then the difference in amount between two friends is:
- If x : y = 8:3, then \((x - y) : (x + y) = ?\)
- If (4x + 5) : (3x + 11) = 13:17, then (5x + 4) : (4x - 1) =?
- If \(4/9 : x = 2/3 : 16/81\), then \(x = ?\)
- If (4x + 5) : (3x + 11) = 13:17, then (5x + 4) : (4x - 1) = ?
If 11.6: x :: x: 2.9, and x > 0, then find the value of x.
Two plumbers, X and Y, are paid a total of ₹770 per day by their employer. If X is paid 140% of the sum paid to Y, then how much is Y paid (in ₹, rounded off to two decimal places) per day?
A workshop mixes coolant concentrate and water in a 3:2 ratio for a machine cooling system. If the total mixture required is 25 liters, how many liters of coolant concentrate are required?
Given the ratio 3:4::6:8, which operation verifies the proportion?
If a : b = 3 : 2 and b : c = 4 : 5, then a : b : c = ?
Important Questions from Ratio and proportion
- An amount is divided between two friends in the ratio 4: 7. If the second part is ₹6 more than the first, then the difference in amount between two friends is:
- If x : y = 8:3, then \((x - y) : (x + y) = ?\)
- If the third proportional of 9 and 60 be x, then what is the value of x?
- If 36% of first number is equal to four-sevenths of second number, what is the ratio of first number to the second number?
- A, B and C invest a sum in the ratio of 61 : 43 : 90, respectively. If they earned a total profit of ₹2,910 at the end of the year, then what is the difference between share of B and C?
