Finding the Combined Ratio $a : b : c$
We are given two ratios:
- $a : b = 7 : 9$
- $b : c = 1 : 12$
Our goal is to find the combined ratio $a : b : c$. To do this, the value representing 'b' must be the same in both ratios.
Calculating the Combined Ratio
- Identify 'b' values: In the first ratio, $b$ corresponds to 9. In the second ratio, $b$ corresponds to 1.
- Equalize 'b': We need to make the 'b' value the same. The least common multiple of 9 and 1 is 9. The first ratio already has $b=9$. We need to adjust the second ratio ($b : c = 1 : 12$) so that $b$ becomes 9.
- Adjust the second ratio: Multiply both parts of the second ratio by 9: $b : c = (1 \times 9) : (12 \times 9)$ $b : c = 9 : 108$
- Combine the ratios: Now we have: $a : b = 7 : 9$ $b : c = 9 : 108$ Since the 'b' value is 9 in both, we can combine them directly.
Therefore, the combined ratio is $a : b : c = 7 : 9 : 108$.
Similar Questions
- If A : B = 3 : 5 and B : C = 4 : 7, then the value of A : B : C is:
- 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?
- If $0.75 : x :: 25 : 8$, then what is the value of $x$?
- If $\frac{A}{4} = \frac{B}{5} = \frac{C}{6}$, then $A : B : C$ is:
- If a map of a city was drawn on a scale of 0.05 centimetre to kilometre, what area would represent a country if it has an area of 8000 square kilometres?
- If A : B = 1 : 3, B : C = 5 : 4 and C : D = 2 : 3, then the value of A : B : C : D will be:
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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:
