For which unit the difference between number of black shirts a... | Mathematics MCQ | Examoogle

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For which unit the difference between number of black shirts and white shirts is maximum ?

None of the above

Correct Answer

📐 MA • Math Ratio Difference MethodMathematicsData Interpretation

Option A

Quick Summary:

Calculate the difference as a fraction of the sum of ratio parts: $(\text{Difference/Sum}) \times \text{Total}$ . For S, the ratio $4:13$ gives a large gap $13-4 = 9$ over sum $17$ , where $9/17$ is roughly $0.53$ . Compare these fractions across units.

📐MAMath SolutionRatio Difference Method

📋 Given

Production units P, Q, R, S, T, U with total shirts and black:white ratio for each.

🔢 Formula Used

Difference=∣a−ba+b∣×Total Shirts\text{Difference} = \left| \frac{a - b}{a + b} \right| \times \text{Total Shirts}Difference=​a+ba−b​​×Total Shirts

⚡ Exam Hall Shortcut / Speed Trick

⚠️ Common Student Trap / Pitfall

Calculating the individual number of shirts for each color instead of using the ratio difference $(\frac{|a-b|}{a+b} \times \text{Total})$ is time-consuming and prone to arithmetic errors.

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Calculate difference for unit P

Ratio is $10:9$ , total is $5225$ . Difference fraction is $\frac{|10^{-9}|}{10+9} = \frac{1}{19}$ . Value is $\frac{5225}{19}$ .

522519=275\frac{5225}{19} = 275195225​=275

Calculate difference for unit Q

Ratio is $9:5$ , total is $3150$ . Difference fraction is $\frac{|9-5|}{9+5} = \frac{4}{14} = \frac{2}{7}$ . Value is $3150 \times \frac{2}{7}$ .

3150×27=9003150 \times \frac{2}{7} = 9003150×72​=900

Calculate difference for unit R

Ratio is $7:8$ , total is $5625$ . Difference fraction is $\frac{|7-8|}{7+8} = \frac{1}{15}$ . Value is $\frac{5625}{15}$ .

562515=375\frac{5625}{15} = 375155625​=375

Calculate difference for unit S

Ratio is $4:13$ , total is $3825$ . Difference fraction is $\frac{|4-13|}{4+13} = \frac{9}{17}$ . Value is $3825 \times \frac{9}{17}$ .

3825×917=225×9=20253825 \times \frac{9}{17} = 225 \times 9 = 20253825×179​=225×9=2025

Calculate difference for units T and U

For T, ratio $4:13$ with total $4875$ (sum $13$ ), difference is $\frac{5}{13} \times 4875 = 1875$ . For U, ratio $11:7$ with total $4950$ (sum $18$ ), difference is $\frac{4}{18} \times 4950 = 1100$ . Comparing all, $2025$ is the highest.

2025>1875>1100>900>375>2752025 > 1875 > 1100 > 900 > 375 > 2752025>1875>1100>900>375>275

✅

A is correct because the difference for unit S is 2025, which is the maximum among all units.

Core Concepts Used

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Ratio and Proportion Data Interpretation Arithmetic Comparison

💡 EXAM TIP

This type of comparative analysis appears frequently in DI sets. Always look for the 'ratio gap' $\frac{a-b}{a+b}$ to quickly rank values without performing full division.

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