Finding the Combined Ratio A : B : C
To find the combined ratio $A : B : C$, we need to make the value representing $B$ the same in both given ratios.
We are given:
- $A : B = 3 : 5$
- $B : C = 4 : 7$
The common term is $B$. The values of $B$ in the ratios are 5 and 4.
Calculate LCM for Common Term B
Find the Least Common Multiple (LCM) of 5 and 4.
LCM(5, 4) = 20
Adjust Ratios to Match B
Adjust the first ratio $A : B = 3 : 5$ so that $B$ becomes 20. Multiply both parts by 4:
$A : B = (3 \times 4) : (5 \times 4) = 12 : 20$
Adjust the second ratio $B : C = 4 : 7$ so that $B$ becomes 20. Multiply both parts by 5:
$B : C = (4 \times 5) : (7 \times 5) = 20 : 35$
Combine the Ratios
Now that $B$ is 20 in both adjusted ratios, we can combine them to find $A : B : C$.
$A : B : C = 12 : 20 : 35$
Thus, the value of $A : B : C$ is $12 : 20 : 35$.
Similar Questions
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- If the third proportional of 8 and 20 be x, then what is the value of x?
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- 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?
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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:
