Question
If 3A = 4B = 8C, what is A : B : C?
The correct answer is
8 : 6 : 3
Solving Ratio A : B : C from 3A = 4B = 8C
To find the ratio A : B : C, we need to express A, B, and C in a common comparable format. We are given the equation:
$3A = 4B = 8C$
Finding the Ratio
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Let the common value of $3A$, $4B$, and $8C$ be equal to the Least Common Multiple (LCM) of the coefficients 3, 4, and 8. The LCM of 3, 4, and 8 is 24.
So, set $3A = 4B = 8C = 24$.
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Now, solve for A, B, and C individually:
- For A: $3A = 24 \implies A = \frac{24}{3} = 8$
- For B: $4B = 24 \implies B = \frac{24}{4} = 6$
- For C: $8C = 24 \implies C = \frac{24}{8} = 3$
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The ratio $A : B : C$ is therefore $8 : 6 : 3$.
Final Ratio
The ratio $A : B : C$ is 8 : 6 : 3.
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Important Questions from Ratio and Proportion (Railways)
If a : b = 3 : 2 and b : c = 3 : 2, then a : b : c = ?
If three numbers are in the ratio 5 : 6 : 8 and their sum is 3800, then the greatest number will be:
- Find the mean proportional between 7.2 and 20.
- What number will be in the place of x?
2.8 : 3.8 : : x : 5.7 - The monthly incomes of two friends Tushar and Salil, are in the ratio 6 : 7 respectively and each of them saves ₹66,000 every month. If the ratio of their monthly expenditure is 2 : 4, find the monthly income of Tushar (in ₹).
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