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
A father distributed two different amounts among his sons P, Q, R and S. First amount was distributed in the ratio 5 : 4 : 3 : 2 and the second amount was distributed in the ratio 6 : 7 : 8 : 9. If the second amount is thrice the first amount, then which son will get the maximum amount?
A sum of ₹420 is divided among A, B, C, and D such that: A : B = 4 : x, B : C = x : 7, C : D = 6 : (x − 3). If B and C together get ₹210, find the value of x.
Given the ratio 3:4::6:8, which operation verifies the proportion?
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?
P, Q and R are three batsmen. The ratios of runs scored by them in a certain match were as follows:
P : Q = 5 : 7 and Q : R = 2 : 3.
If they scored a total of 765 runs, then find the number of runs scored by R.- If ₹ 87 was divided between James and Radha in the ratio 1 : 2, how much money did Radha get?
- If 3 dozen guavas cost ₹ 90, how many guavas can be bought for ₹ 240?
Important Questions from Ratio and proportion
A’s marks in Mathematics are directly proportional to practice time. In 6 hours of practice, A gets 70 marks. What should be the practice time (approximately) to get 90 marks?
The average of the areas of 2 similar triangles is 706.5 m2 whose perimeters are in the ratio of 6 : 11. What is 20% of the difference (in m2) in areas of both triangles?
In a triangle ABC, D and E are two points on sides AB and AC, respectively, such that DE is parallel to BC and AD : DB = 3 : 5. If AC = 5.6 cm, then find the value (in cm) of AE.
In a triangle ABC, P and Q are two points on AB and AC, respectively, such that PQ is parallel to BC. If AC = 5QC, then the ratio PQ : BC is equal to:
Find the mean proportional between 25 and 81.
