A can complete work in 15 days, and B in 20 days. If both work... | Mathematics MCQ | Examoogle

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A can complete work in 15 days, and B in 20 days. If both work together for 4 days, what fraction of the work remains?

$\frac{7}{15}$

$\frac{8}{15}$

$\frac{11}{15}$

$\frac{13}{15}$

Correct Answer

📐 MA • Math LCM MethodMathematicsTime and Work

Option B

$\frac{8}{15}$

Quick Summary:

Calculate LCM of 15 and 20 (60). Efficiency of A is 4 units/day and B is 3 units/day. In 4 days, they complete $4 \times (4+3) = 28$ units. Remaining work is $60 - 28 = 32$ units. Fraction remaining is $\frac{32}{60} = \frac{8}{15}$ .

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📐MAMath SolutionLCM Method

📋 Given

A completes work in 15 days, B in 20 days. Both work together for 4 days.

🔢 Formula Used

Work Done=Time×(A’s efficiency+B’s efficiency)\text{Work Done} = \text{Time} \times (\text{A's efficiency} + \text{B's efficiency})Work Done=Time×(A’s efficiency+B’s efficiency)

⚡ Exam Hall Shortcut / Speed Trick

⚠️ Common Student Trap / Pitfall

Students often calculate the fraction of work completed ( $\frac{28}{60} = \frac{7}{15}$ ) and mark Option A, forgetting the question asks for the fraction that remains.

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Calculate LCM and Efficiencies

Assume total work as the LCM of 15 and 20, which is 60 units. A's efficiency is $\frac{60}{15} = 4$ units/day and B's efficiency is $\frac{60}{20} = 3$ units/day.

Total Work=60,Aeff=4,Beff=3\text{Total Work} = 60, \quad A_{eff} = 4, \quad B_{eff} = 3Total Work=60,Aeff​=4,Beff​=3

Calculate work done in 4 days

Both work together for 4 days with a combined efficiency of $4 + 3 = 7$ units/day.

4×(4+3)=28 units4 \times (4 + 3) = 28 \text{ units}4×(4+3)=28 units

Calculate remaining work fraction

Subtract the work done from total work: $60 - 28 = 32$ . The remaining fraction is the remaining work divided by total work.

3260=815\frac{32}{60} = \frac{8}{15}6032​=158​

✅

B is correct because the remaining work is 32 units out of 60, which simplifies to 8/15.

Core Concepts Used

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Time and Work LCM Method Efficiency Work Fraction

💡 EXAM TIP

This unit-based approach is applicable to Pipe and Cistern problems as well, where 'units' represent volume and 'efficiency' represents the rate of water flow.

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