If 12 men can reap a field in 8 days working 7 hours/day, then... | Mathematics MCQ | Examoogle

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MathematicsArithmetic

If 12 men can reap a field in 8 days working 7 hours/day, then how many hours/day must 16 men work to reap the same field in 6 days?

Correct Answer

⚙️ TE • Technical Direct FormulaMathematicsArithmetic

Option D

Quick Summary:

Use the work proportionality: $12 \times 8 \times 7 = 16 \times 6 \times H_{2}$ . Since $16 \times 6 = 96$ and $12 \times 8 = 96$ , the hours must be identical to the original value: $7$ .

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📐MAMath SolutionDirect Formula

📋 Given

12 men reap a field in 8 days working 7 hours/day; 16 men need to reap the same field in 6 days.

🔢 Formula Used

M1×D1×H1W1=M2×D2×H2W2\frac{M_{1} \times D_{1} \times H_{1}}{W_{1}} = \frac{M_{2} \times D_{2} \times H_{2}}{W_{2}}W1​M1​×D1​×H1​​=W2​M2​×D2​×H2​​

⚡ Exam Hall Shortcut / Speed Trick

Use the work proportionality: $12 \times 8 \times 7 = 16 \times 6 \times H_{2}$ . Since $16 \times 6 = 96$ and $12 \times 8 = 96$ , the hours must be identical to the original value: $7$ .

⚠️ Common Student Trap / Pitfall

Many students mistake the relationship as directly proportional for all variables, forgetting that man-power and time are inversely proportional to hours per day.

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Identify given parameters

Set the parameters for the first group ( $M_{1}=12, D_{1}=8, H_{1}=7$ ) and the second group ( $M_{2}=16, D_{2}=6, H_{2}=x$ ).

M1=12,D1=8,H1=7,M2=16,D2=6,H2=xM_{1}=12, D_{1}=8, H_{1}=7, M_{2}=16, D_{2}=6, H_{2}=xM1​=12,D1​=8,H1​=7,M2​=16,D2​=6,H2​=x

Apply Chain Rule formula

Since the work $W$ is the same for both cases ( $W_{1}=W_{2}=1$ ), the formula simplifies to the product of men, days, and hours.

12×8×7=16×6×x12 \times 8 \times 7 = 16 \times 6 \times x12×8×7=16×6×x

Calculate the unknown variable

Simplify the equation: $672 = 96x$ . Solving for $x$ gives $x = \frac{672}{96} = 7$ .

x=12×8×716×6=7x = \frac{12 \times 8 \times 7}{16 \times 6} = 7x=16×612×8×7​=7

✅

D is correct because the calculated number of hours required per day is 7.

Core Concepts Used

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Chain Rule Inverse Variation Work-Time Equivalence

💡 EXAM TIP

This concept of 'Man-Days' is the foundation for solving complex piping and cistern problems in Speed, Time, and Distance topics.

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