Solving for the Combined Ratio A : B : C : D
To find the combined ratio A : B : C : D, we need to make the common terms in the given ratios equal.
Step 1: Combine A : B and B : C
We are given:
- A : B = 1 : 3
- B : C = 5 : 4
The common term is B. To make the B values equal, we find the Least Common Multiple (LCM) of 3 and 5, which is 15.
- Multiply A : B by 5: A : B = (1 \times 5) : (3 \times 5) = 5 : 15
- Multiply B : C by 3: B : C = (5 \times 3) : (4 \times 3) = 15 : 12
Now, B has the same value (15) in both ratios. The combined ratio A : B : C is:
A : B : C = 5 : 15 : 12
Step 2: Combine A : B : C and C : D
We now have:
- A : B : C = 5 : 15 : 12
- C : D = 2 : 3
The common term is C. To make the C values equal, we find the LCM of 12 and 2, which is 12.
- A : B : C is already 5 : 15 : 12 (C is 12).
- Multiply C : D by 6: C : D = (2 \times 6) : (3 \times 6) = 12 : 18
Now, C has the same value (12) in both ratios. The combined ratio A : B : C : D is:
A : B : C : D = 5 : 15 : 12 : 18
Conclusion
Therefore, the value of A : B : C : D is 5 : 15 : 12 : 18.
Similar Questions
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- If $a : b :: 3 : 4$ then the value of the expression $\frac{5a - 3b}{7a + 2b}$ is:
- If the third proportional of 8 and 20 be x, then what is the value of x?
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Important Questions from Ratio and Proportion
In a mixture of 156 litres, the ratio of milk and water is 7 : 6. How much water should be added to make the ratio 14 : 13?
If the ratio of the first to second number is 3 : 4 and that of the second to the third number is 8 : 5, and sum of three numbers is 190 then the third number is:
The third proportional to 9 and 15 is:
The average age of 3 persons is 30 years.If their ages are in the ratio of 3 : 5 : 7 respectively, then the age of the eldest person is:
The income of A and B are in the ratio 5 : 3. The expenses of A, B and C are in the ratio of 8 : 5 : 2. If C spends 2000 and B saves ₹ 700, then A saves:
