If 25 persons can complete 5 units of work by working 15 hours... | Mathematics MCQ

MathematicsPrevious Year Paper 2024

If 25 persons can complete 5 units of work by working 15 hours per day in 8 days, then how many days will be required for 12 persons to complete 10 units of work by working 20 hours per day?

20 days

25 days

22 days

24 days

Correct Answer

📐 MA • Math Direct FormulaMathematicsPrevious Year Paper 2024

Option B

25 days

Quick Summary:

Use the work-time formula $\frac{M_1 D_1 H_1}{W_1} = \frac{M_2 D_2 H_2}{W_2}$ and substitute directly to solve for $D_2$ in a single equation.

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📐MAMath SolutionDirect Formula

📋 Given

Case 1: $M_1 = 25$ persons, $H_1 = 15$ hours/day, $W_1 = 5$ units, $D_1 = 8$ days. Case 2: $M_2 = 12$ persons, $H_2 = 20$ hours/day, $W_2 = 10$ units, $D_2 =?$ 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-time formula $\frac{M_1 D_1 H_1}{W_1} = \frac{M_2 D_2 H_2}{W_2}$ and substitute directly to solve for $D_2$ in a single equation.

⚠️ Common Student Trap / Pitfall

Placing work units ( $W$ ) in the numerator instead of the denominator. Work done must always be in the denominator.

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Identify the standard work-time formula

The general formula relating men, days, hours, and work is given by: $\frac{M_1 \times D_1 \times H_1}{W_1} = \frac{M_2 \times D_2 \times H_2}{W_2}$

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​​

Substitute the given values into the formula

Substitute $M_1 = 25$ , $D_1 = 8$ , $H_1 = 15$ , $W_1 = 5$ and $M_2 = 12$ , $H_2 = 20$ , $W_2 = 10$ : $\frac{25 \times 8 \times 15}{5} = \frac{12 \times D_2 \times 20}{10}$

25×8×155=12×D2×2010\frac{25 \times 8 \times 15}{5} = \frac{12 \times D_2 \times 20}{10}525×8×15​=1012×D2​×20​

Simplify both sides of the equation

LHS: $\frac{3000}{5} = 600$ . RHS: $\frac{240 \times D_2}{10} = 24 \times D_2$ .

600=24×D2600 = 24 \times D_2600=24×D2​

Solve for D2

Divide 600 by 24 to find the number of days required: $D_2 = \frac{600}{24} = 25$

D2=25 daysD_2 = 25 \text{ days}D2​=25 days

✅

B is correct because calculating using the work-time formula yields exactly 25 days.

Core Concepts Used

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Work and Time Proportion Chain Rule Formula Inverse and Direct Variation

💡 EXAM TIP

This chain rule concept is widely applicable across pipes & cisterns and workforce management problems.

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