Out of the total number of chairs manufactured ge in January, ... | Mathematics MCQ | Examoogle

MathematicsArithmetic

Out of the total number of chairs manufactured ge in January, 20% of the chairs are unsold. If the ratio of the number of office chairs to wheel chairs unsold in January is 5 ∶ 4, then find the number of wheel chairs sold in January.

690

820

510

780

None of the above

Correct Answer

⚙️ TE • Technical Ratio Proportion AnalysisMathematicsArithmetic

Option D

780

Quick Summary:

Calculate January total as $0.27 \times 5000 = 1350$ . Unsold is 270. Since unsold ratio is Office:Wheel = 5:4, Wheel unsold is $\frac{4}{9} \times 270 = 120$ . Total wheel chairs = $\frac{2}{3} \times 1350 = 900$ . Sold = $900 - 120 = 780$ .

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📐MAMath SolutionRatio Proportion Analysis

📋 Given

Total chairs = 5000, January production = 27% of 5000, Ratio Wheel:Office = 2:1. Unsold chairs = 20% of January total, Unsold ratio Office:Wheel = 5:4.

🔢 Formula Used

Value=(Ratio PartTotal Ratio Parts)×Total Amount\text{Value} = \left(\frac{\text{Ratio Part}}{\text{Total Ratio Parts}}\right) \times \text{Total Amount}Value=(Total Ratio PartsRatio Part​)×Total Amount

⚡ Exam Hall Shortcut / Speed Trick

⚠️ Common Student Trap / Pitfall

Students often swap the ratio of Office:Wheel vs Wheel:Office for the unsold part or apply the 20% to the wrong total.

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Calculate total chairs in January

Total chairs in January is $27\% \times 5000 = 0.27 \times 5000 = 1350$ .

TotalJan=1350\text{Total}_{\text{Jan}} = 1350TotalJan​=1350

Calculate number of wheel chairs and office chairs

Ratio is $2:1$ . Total parts $2+1=3$ . Wheel chairs = $\frac{2}{3} \times 1350 = 900$ . Office chairs = $\frac{1}{3} \times 1350 = 450$ .

Wheeltotal=900,Officetotal=450\text{Wheel}_{\text{total}} = 900, \quad \text{Office}_{\text{total}} = 450Wheeltotal​=900,Officetotal​=450

Calculate total unsold chairs in January

Unsold = $20\% \times 1350 = 0.20 \times 1350 = 270$ .

Unsoldtotal=270\text{Unsold}_{\text{total}} = 270Unsoldtotal​=270

Calculate unsold wheel chairs

Unsold ratio Office:Wheel is $5:4$ . Total parts $5+4=9$ . Wheel chairs unsold = $\frac{4}{9} \times 270 = 4 \times 30 = 120$ .

Unsoldwheel=120\text{Unsold}_{\text{wheel}} = 120Unsoldwheel​=120

Calculate sold wheel chairs

Sold wheel chairs = Total wheel chairs - Unsold wheel chairs = $900 - 120 = 780$ .

Soldwheel=900−120=780\text{Sold}_{\text{wheel}} = 900 - 120 = 780Soldwheel​=900−120=780

✅

D is correct because the total wheel chairs in January is 900 and the number of unsold wheel chairs is 120, leaving 780 sold.

Core Concepts Used

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Percentage Calculation Ratio Division Inventory Management Logic

💡 EXAM TIP

This problem uses Data Interpretation skills; always reduce ratios first to simplify calculations.

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