If a : b = 3 : 2 and b : c = 4 : 5, then a : b : c = ?
6 : 4 : 5
Understanding the Ratio Problem
The question asks us to find the combined ratio \(a : b : c\) given two separate ratios: \(a : b = 3 : 2\) and \(b : c = 4 : 5\). To find the combined ratio, we need to make sure the value representing 'b' is the same in both given ratios.
Combining Ratios Step-by-Step
We are given:
- Ratio 1: \(a : b = 3 : 2\)
- Ratio 2: \(b : c = 4 : 5\)
Notice that the term 'b' is common to both ratios. However, in Ratio 1, \(b\) is represented by 2, and in Ratio 2, \(b\) is represented by 4. We need to make these values equal.
- Find a Common Value for 'b': The least common multiple (LCM) of 2 and 4 is 4. We want 'b' to be 4 in both ratios.
- Adjust Ratio 1: The first ratio is \(a : b = 3 : 2\). To make 'b' equal to 4, we need to multiply both parts of the ratio by 2 (since \(2 \times 2 = 4\)). \( a : b = (3 \times 2) : (2 \times 2) = 6 : 4 \)
- Keep Ratio 2: The second ratio is \(b : c = 4 : 5\). The value for 'b' is already 4, so we don't need to change this ratio.
- Combine the Ratios: Now we have \(a : b = 6 : 4\) and \(b : c = 4 : 5\). Since 'b' is represented by 4 in both, we can combine them directly into the \(a : b : c\) ratio. \( a : b : c = 6 : 4 : 5 \)
Final Combined Ratio
By adjusting the first ratio so that the value of 'b' matches the second ratio, we successfully combined them. The final combined ratio \(a : b : c\) is \(6 : 4 : 5\).
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?
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?
