If 15 men can build a wall 162m long in 8 days, how many men w... | Mathematics MCQ | Examoogle

Examoogle • User • info@examoogle.com • EE-2024-8821

Chapter 1 of 12 • Page 1 of 248🔒 Protected PDF • Watermarked

MathematicsTime and Work

If 15 men can build a wall 162m long in 8 days, how many men will be required to build a similar wall 324m long in 6 days?

Correct Answer

📐 MA • Math Direct FormulaMathematicsTime and Work

Option B

Quick Summary:

Observe the ratio: Length doubled from $162m$ to $324m$ ( $2\times$ ) and time decreased from $8$ days to $6$ days ( $0.75\times$ ). Thus, men needed is $15 \times 2 \div 0.75 = 40$ .

🎯

Crack Time and Work with Examoogle SuperTeachers

Get Free Demo Classes & Live Mocks →

📐MAMath SolutionDirect Formula

📋 Given

For Case 1: Men ( $M_1$ ) = 15, Length ( $W_1$ ) = 162m, Days ( $D_1$ ) = 8. For Case 2: Men ( $M_2$ ) =?, Length ( $W_2$ ) = 324m, Days ( $D_2$ ) = 6.

🔢 Formula Used

M1×D1W1=M2×D2W2\frac{M_1 \times D_1}{W_1} = \frac{M_2 \times D_2}{W_2}W1​M1​×D1​​=W2​M2​×D2​​

⚡ Exam Hall Shortcut / Speed Trick

Observe the ratio: Length doubled from $162m$ to $324m$ ( $2\times$ ) and time decreased from $8$ days to $6$ days ( $0.75\times$ ). Thus, men needed is $15 \times 2 \div 0.75 = 40$ .

⚠️ Common Student Trap / Pitfall

Students often multiply the work length incorrectly or forget that work done ( $W$ ) must always be in the denominator of the work formula.

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Identify given variables

Identify the parameters for the work equation using the formula $M_1 D_1 / W_1 = M_2 D_2 / W_2$ .

M1=15,D1=8,W1=162;M2=?,D2=6,W2=324M_1=15, D_1=8, W_1=162; M_2=?, D_2=6, W_2=324M1​=15,D1​=8,W1​=162;M2​=?,D2​=6,W2​=324

Apply the Chain Rule formula

Substitute the given values into the formula to find the number of men $M_2$ .

15×8162=M2×6324\frac{15 \times 8}{162} = \frac{M_2 \times 6}{324}16215×8​=324M2​×6​

Solve for $M_2$

Simplify the expression: note that $324 / 162 = 2$ . Rearrange to solve for $M_2$ .

M2=15×8×324162×6=120×26=2406=40M_2 = \frac{15 \times 8 \times 324}{162 \times 6} = \frac{120 \times 2}{6} = \frac{240}{6} = 40M2​=162×615×8×324​=6120×2​=6240​=40

✅

B is correct because the calculation $M_2 = 40$ matches the requirement to complete twice the work in less time.

Core Concepts Used

Click any tag to open in AI Tutor

Chain Rule Inverse Proportion Direct Proportion

💡 EXAM TIP

This chain rule concept is identical to solving Pipe and Cistern problems where 'Work' is replaced by 'Volume' or 'Capacity'.

Was this solution helpful?

⚡ Practice on Android App · 4.8 ★

Solve 10,000+ More Questions with AI Tutor

Get instant step-by-step AI explanations, full shift Previous Year Papers (SSC GD, RRB, SSC JE), and regional rank analysis on the official Examoogle App.

Free Download • 100K+ Aspirants

Discussion (0)

Loading discussion...

Prev Next

Correct Answer

Solve 10,000+ More Questions with AI Tutor

Related Questions

Discussion (0)