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 \(6 : 4 : 5\).
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Important Questions from Ratio and proportion
A sum of Rs. 2,500 is distributed among X, Y and Z in the ratio 1/2 : 3/4 : 5/6 . What is the difference between the maximum share and the minimum share?
In a class, there are three groups A, B and C. If one student from group A and two students from group B are shifted to group C, then what happens to the average weight of the students of the class?
How many different sums can be formed with the denominations Rs. 50, Rs. 100, Rs. 200, Rs. 500 and Rs. 2,000 taking at least three denominations at a time?
In a 500 metres race, B starts 45 metres ahead of A, but A wins the race while B is still 35 metres behind. What is the ratio of the speeds of A to B assuming that both start at the same time?
The monthly incomes of Peter and Paul are in the ratio of 4 : 3. Their expenses are in the ratio of 3 : 2. If each saves Rs. 6,000 at the end of the month, their monthly incomes respectively are (in Rs.)
