If A : B = 2 : 3, B : C = 3 : 4 and C : D = 3 : 5 then value of A : B : C : D is:
6 : 9 : 12 : 20
Finding the Combined Ratio A : B : C : D
This problem requires us to determine the combined ratio A : B : C : D. We are given three separate ratios that link these variables: A : B, B : C, and C : D. To find the combined ratio, we need to make sure the terms common to multiple ratios have the same numerical value.
Given Ratios
The initial ratios provided are:
A : B = 2 : 3B : C = 3 : 4C : D = 3 : 5
Method for Combining Ratios
The process involves linking the ratios through shared variables. We start by combining the first two ratios and then incorporate the third ratio.
Step 1: Combining A : B and B : C
First, let's look at the ratios involving A, B, and C:
A : B = 2 : 3B : C = 3 : 4
The variable B is common to both ratios. In the first ratio, B corresponds to 3. In the second ratio, B also corresponds to 3. Since the value for B is the same in both ratios, we can directly combine them.
Therefore, the combined ratio A : B : C is:
A : B : C = 2 : 3 : 4
Step 2: Combining A : B : C with C : D
Next, we combine the ratio found in Step 1 with the third given ratio:
A : B : C = 2 : 3 : 4C : D = 3 : 5
The variable C is common here. In the ratio A : B : C, C corresponds to 4. In the ratio C : D, C corresponds to 3.
The values for C (4 and 3) are different. To combine these ratios, we must make the value for C the same in both. We do this by finding the Least Common Multiple (LCM) of the two values, 4 and 3.
The LCM of 4 and 3 is 12.
Now, we adjust each ratio to make the value for C equal to 12:
- For the ratio
A : B : C = 2 : 3 : 4, we multiply each part by 3 (because12 / 4 = 3):A : B : C = (2 \times 3) : (3 \times 3) : (4 \times 3) = 6 : 9 : 12 - For the ratio
C : D = 3 : 5, we multiply each part by 4 (because12 / 3 = 4):C : D = (3 \times 4) : (5 \times 4) = 12 : 20
With the value for C now matching (12) in both adjusted ratios, we can combine them to find the final ratio A : B : C : D:
A : B : C : D = 6 : 9 : 12 : 20
Final Answer Verification
The resulting combined ratio is 6 : 9 : 12 : 20. Comparing this with the given options, we find that it matches the fourth option.
Similar Questions
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Important Questions from Ratio and Proportion
The cost of a diamond is directly proportional to the square of its weight. The cost of a 14 gm diamond is Rs. 2560. This diamond got broken down into two pieces in the ratio of 5 ∶ 9. How much loss percent is incurred due to this breakage ? (Correct to two decimal places)
Atul purchased Bread costing Rs.20 and gave a 100 rupee note to the shopkeeper. The shopkeeper gave the balance money in coins of denomination Rs.2, Rs.5 and Rs.10. If these coins are in the ratio 5 ∶ 4 ∶ 1, then how many Rs.5 coins did the shopkeeper give?
A person divides a certain amount among his three sons in the ratio of 3 ∶ 4 ∶ 5. If he had divided this amount in the ratio of 1/3,1/4,1/5, his son, who had got the lowest share earlier, would get Rs.1,188 more. Find the amount (in Rs).
In a school 3/8 of the number of students are girls and the rest are boys. One-third of the number of boys are below 10 years and 2/3 the number if girls are also below 10 years. If the number of students of age 10 or more years is 260. then the number of boys in the school is:
If a : b : c = \(\frac{1}{4} : \frac{1}{3} : \frac{1}{2}, \) then \( \ \frac{a}{b} : \frac{b}{c} : \frac{c}{a} = ?\)
