Ratio Comparison Technique
To find the smallest ratio among the given options, we convert each ratio into its decimal form. This allows for a direct numerical comparison.
Steps to Find the Smallest Ratio
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Convert Ratios to Decimals: Express each ratio \(a : b\) as a fraction \(\frac{a}{b}\) and calculate its decimal value.
- For \(4 : 7\), the fraction is \(\frac{4}{7}\). \( \frac{4}{7} \approx 0.5714 \).
- For \(7 : 10\), the fraction is \(\frac{7}{10}\). \( \frac{7}{10} = 0.7 \).
- For \(5 : 8\), the fraction is \(\frac{5}{8}\). \( \frac{5}{8} = 0.625 \).
- For \(6 : 9\), the fraction is \(\frac{6}{9}\). Simplifying gives \(\frac{2}{3}\). \( \frac{2}{3} \approx 0.6667 \).
- Compare Decimal Values: List the decimal values obtained: \(0.5714\), \(0.7\), \(0.625\), \(0.6667\).
- Identify the Smallest Value: Compare the decimal values to find the minimum. The values in ascending order are: \(0.5714 < 0.625 < 0.6667 < 0.7\). The smallest decimal value is approximately \(0.5714\).
- Determine the Smallest Ratio: The decimal \(0.5714\) corresponds to the ratio \(4 : 7\).
Therefore, the ratio \(4 : 7\) is the smallest among the given options.
Similar Questions
- An amount is divided between two friends in the ratio 4: 7. If the second part is ₹6 more than the first, then the difference in amount between two friends is:
- If x : y = 8:3, then \((x - y) : (x + y) = ?\)
- If (4x + 5) : (3x + 11) = 13:17, then (5x + 4) : (4x - 1) =?
- If \(4/9 : x = 2/3 : 16/81\), then \(x = ?\)
- If (4x + 5) : (3x + 11) = 13:17, then (5x + 4) : (4x - 1) = ?
If 11.6: x :: x: 2.9, and x > 0, then find the value of x.
Two plumbers, X and Y, are paid a total of ₹770 per day by their employer. If X is paid 140% of the sum paid to Y, then how much is Y paid (in ₹, rounded off to two decimal places) per day?
A workshop mixes coolant concentrate and water in a 3:2 ratio for a machine cooling system. If the total mixture required is 25 liters, how many liters of coolant concentrate are required?
Given the ratio 3:4::6:8, which operation verifies the proportion?
If a : b = 3 : 2 and b : c = 4 : 5, then a : b : c = ?
Important Questions from Ratio and proportion
- An amount is divided between two friends in the ratio 4: 7. If the second part is ₹6 more than the first, then the difference in amount between two friends is:
- If x : y = 8:3, then \((x - y) : (x + y) = ?\)
- If the third proportional of 9 and 60 be x, then what is the value of x?
- If 36% of first number is equal to four-sevenths of second number, what is the ratio of first number to the second number?
- A, B and C invest a sum in the ratio of 61 : 43 : 90, respectively. If they earned a total profit of ₹2,910 at the end of the year, then what is the difference between share of B and C?
