What is the respective ratio between the number of female regi... | Mathematics MCQ | Examoogle

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What is the respective ratio between the number of female register in Hyderabad and male register in Patna?

11:7

13:4

11:3

12:7

None of the above

Correct Answer

📐 MA • Math Ratio MethodMathematicsData Interpretation

Option B

13:4

Quick Summary:

Calculate individual required parts directly: $F_{\text{Hyd}} = \frac{13}{12+13} \times 2500$ and $M_{\text{Pat}} = \frac{4}{4+3} \times 700$ . Simplify before multiplying to save time.

📐MAMath SolutionRatio Method

📋 Given

Hyderabad workshop registrations = 2500, ratio (M:F) = 12:13. Patna workshop registrations = 700, ratio (M:F) = 4:3.

🔢 Formula Used

Value=Total×Ratio PartSum of Ratios\text{Value} = \text{Total} \times \frac{\text{Ratio Part}}{\text{Sum of Ratios}}Value=Total×Sum of RatiosRatio Part​

⚡ Exam Hall Shortcut / Speed Trick

Calculate individual required parts directly: $F_{\text{Hyd}} = \frac{13}{12+13} \times 2500$ and $M_{\text{Pat}} = \frac{4}{4+3} \times 700$ . Simplify before multiplying to save time.

⚠️ Common Student Trap / Pitfall

Students often confuse the male-to-female ratio order for the requested female-to-male comparison or use the wrong total city registration count.

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Calculate female registrations in Hyderabad

The total registrations for Hyderabad are 2500 with a ratio of male to female as 12:13. The female portion is $\frac{13}{12+13} = \frac{13}{25}$ .

FemaleHyd=2500×1325=1300\text{Female}_{\text{Hyd}} = 2500 \times \frac{13}{25} = 1300FemaleHyd​=2500×2513​=1300

Calculate male registrations in Patna

The total registrations for Patna are 700 with a ratio of male to female as 4:3. The male portion is $\frac{4}{4+3} = \frac{4}{7}$ .

MalePat=700×47=400\text{Male}_{\text{Pat}} = 700 \times \frac{4}{7} = 400MalePat​=700×74​=400

Find the ratio

The ratio between female Hyderabad ( $1300$ ) and male Patna ( $400$ ) is $\frac{1300}{400}$ .

Ratio=1300400=134=13:4\text{Ratio} = \frac{1300}{400} = \frac{13}{4} = 13:4Ratio=4001300​=413​=13:4

✅

B is correct because the calculation for Hyderabad females is 1300 and Patna males is 400, resulting in the ratio 13:4.

Core Concepts Used

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Ratio and Proportion Data Interpretation Part-Whole relationship

💡 EXAM TIP

This type of ratio distribution is foundational for solving mixture and alligation problems in competitive quantitative aptitude sections.

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