Solving the Ratio Equation
The problem provides a ratio equality and asks for the value of another ratio. We first need to find the value of 'x' using the given equation.
Given ratio equation:
\( \frac{4x + 5}{3x + 11} = \frac{13}{17} \)Finding the Value of 'x'
To find 'x', we cross-multiply the terms:
- Cross-multiplication: \(17 \times (4x + 5) = 13 \times (3x + 11)\)
- Expand both sides: \(68x + 85 = 39x + 143\)
- Group 'x' terms on one side and constants on the other: \(68x - 39x = 143 - 85\)
- Simplify the equation: \(29x = 58\)
- Solve for 'x': \(x = \frac{58}{29}\) \(x = 2\)
Calculating the Target Ratio
Now, substitute the value \(x=2\) into the expression \((5x + 4) : (4x - 1)\):
- Calculate the first term: \(5x + 4 = 5(2) + 4 = 10 + 4 = 14\)
- Calculate the second term: \(4x - 1 = 4(2) - 1 = 8 - 1 = 7\)
The required ratio is \(14 : 7\).
Simplifying the Ratio
Simplify the ratio \(14 : 7\) by dividing both terms by their greatest common divisor, which is 7:
\( \frac{14}{7} = \frac{2}{1} \)Therefore, the ratio \((5x + 4) : (4x - 1)\) is \(2 : 1\).
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 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 = ?
Study the following graph and answer the given question.
The graph shows the height of five students in a class.
What is the respective ratio between the height of Amit and the height of Rahul?
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?
