If the total number of balloons manufactured on Thursday is 25... | Mathematics MCQ | Examoogle

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MathematicsData Interpretation

If the total number of balloons manufactured on Thursday is 25% less than that of on Wednesday and the ratio of the total I number of purple, green and grey colour balloons manufactured on Thursday is 4 ∶ 3 ∶ 2 respectively, then find the total number of purple colour balloons manufactured on Thursday.

260

240

280

220

None of the above

Correct Answer

📐 MA • Math Ratio MethodMathematicsData Interpretation

Option B

240

Quick Summary:

Calculate Wednesday total (720), subtract 25% (180) to get Thursday total (540). Since the ratio of purple:green:grey is 4:3:2, sum of parts = 9. Purple part = (4/9) * 540 = 240.

📐MAMath SolutionRatio Method

📋 Given

Wednesday total purple = 150, grey = 240. Green = 150 * (11/5) = 330. Total Wednesday = 150 + 240 + 330 = 720. Thursday total = 25% less than Wednesday.

🔢 Formula Used

Thursday Total=Wednesday Total×(1−25%)=Wednesday Total×0.75\text{Thursday Total} = \text{Wednesday Total} \times (1 - 25\%) = \text{Wednesday Total} \times 0.75Thursday Total=Wednesday Total×(1−25%)=Wednesday Total×0.75

⚡ Exam Hall Shortcut / Speed Trick

Calculate Wednesday total (720), subtract 25% (180) to get Thursday total (540). Since the ratio of purple:green:grey is 4:3:2, sum of parts = 9. Purple part = (4/9) * 540 = 240.

⚠️ Common Student Trap / Pitfall

Students often calculate the Wednesday total incorrectly by failing to include all three colors (purple, green, grey) or incorrectly calculating the green balloon count.

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Calculate Wednesday Total

Purple = 150, Grey = 240. Given Purple is 5/11th of Green, so Green = $150 \times \frac{11}{5} = 330$ . Total Wednesday = $150 + 240 + 330 = 720$ .

TotalW=150+240+330=720\text{Total}_W = 150 + 240 + 330 = 720TotalW​=150+240+330=720

Calculate Thursday Total

Thursday total is 25% less than 720. So, $720 \times (1 - 0.25) = 720 \times 0.75 = 540$ .

TotalTh=720×0.75=540\text{Total}_{Th} = 720 \times 0.75 = 540TotalTh​=720×0.75=540

Apply Ratio to find Purple Balloons

The ratio is 4:3:2 for P:G:Gr. Sum of ratio parts = $4 + 3 + 2 = 9$ . Purple portion = $\frac{4}{9} \times 540$ .

PurpleTh=49×540=240\text{Purple}_{Th} = \frac{4}{9} \times 540 = 240PurpleTh​=94​×540=240

✅

B is correct because the total number of balloons on Thursday is 540, and the purple share of 4/9 results in 240 balloons.

Core Concepts Used

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Data Interpretation Ratio and Proportion Percentage Calculation

💡 EXAM TIP

Always ensure you account for all components in a sum when calculating a 'Total' for subsequent comparisons; missing one category is the most common reason for failure in DI sets.

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