If A can do 1/3 of a work in 5 days and B can do 2/5 of the sa... | Mathematics MCQ | Examoogle

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MathematicsTime and Work

If A can do 1/3 of a work in 5 days and B can do 2/5 of the same work in 10 days, how long will they take to finish the work together?

7.5 $\text{ days}$

8.5 $\text{ days}$

9.5 $\text{ days}$

10 $\text{ days}$

Correct Answer

📐 MA • Math LCM MethodMathematicsTime and Work

Option A

7.5 $\text{ days}$

Quick Summary:

Calculate individual total time: A takes $5 \times 3 = 15$ days, B takes $10 \times \frac{5}{2} = 25$ days. Use $\frac{A \times B}{A + B} = \frac{15 \times 25}{15 + 25} = \frac{375}{40} = 9.375$ . Wait, re-evaluating: A=15, B=25. $\frac{375}{40} = 9.375$ . Actually, the question states A does 1/3 in 5 days (15 total) and B does 2/5 in 10 days (25 total).

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📐MAMath SolutionLCM Method

📋 Given

A does 1/3 of the work in 5 days, B does 2/5 of the work in 10 days.

🔢 Formula Used

T=WEA+EBT = \frac{W}{E_A + E_B}T=EA​+EB​W​

⚡ Exam Hall Shortcut / Speed Trick

⚠️ Common Student Trap / Pitfall

Students often assume B does the work in 10 days, forgetting to calculate the total time for the full work, i.e., $10 \times \frac{5}{2} = 25$ days.

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Calculate total time for A

If A does $1/3$ work in $5$ days, total time is $5 \times 3 = 15$ days.

TA=15 daysT_A = 15 \text{ days}TA​=15 days

Calculate total time for B

If B does $2/5$ work in $10$ days, total time is $10 \times \frac{5}{2} = 25$ days.

TB=25 daysT_B = 25 \text{ days}TB​=25 days

Find combined rate and total time

Using the product-sum formula: $\frac{15 \times 25}{15 + 25} = \frac{375}{40}$ .

37540=9.375 days\frac{375}{40} = 9.375 \text{ days}40375​=9.375 days

✅

The calculated result is 9.375 days, which suggests an error in the provided official option A (7.5 days) as 9.375 does not match the options exactly.

Core Concepts Used

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Work-Time Efficiency Fractional Work Rate LCM Method

💡 EXAM TIP

Always convert partial work durations to full work durations ( $1$ unit) before applying combined rate formulas.

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