A మరియు B ఒక పనిని వరుసగా 12 రోజులు మరియు 18 రోజులలో పూర్తి చే... | Mathematics MCQ (తెలుగు) | Examoogle

MathematicsTime and Work

A మరియు B ఒక పనిని వరుసగా 12 రోజులు మరియు 18 రోజులలో పూర్తి చేయగలరు. వారు కలిసి 6 రోజులు పని చేస్తే, పనిలో ఎంత భాగం మిగిలి ఉంటుంది?

పనిలో $\frac{1}{9}$

పనిలో $\frac{1}{7}$

పనిలో $\frac{1}{2}$

పనిలో $\frac{1}{6}$

Correct Answer

📐 MA • Math LCM MethodMathematicsTime and Work

పనిలో $\frac{1}{6}$

Quick Summary:

Calculate LCM of (12, 18) = 36 units. A's efficiency = 3, B's efficiency = 2. Combined = 5. In 6 days, they finish 5 × 6 = 30 units. Left = 36 - 30 = 6 units. Fraction left = 6/36 = 1/6.

📐MAMath SolutionLCM Method

📋 Given

Time taken by A = 12 days, Time taken by B = 18 days, Duration worked together = 6 days.

🔢 Formula Used

Work=TimeworkedTotaltime\text{Work} = \frac{Time_{worked}}{Total_{time}}Work=Totaltime​Timeworked​​

⚡ Exam Hall Shortcut / Speed Trick

Calculate LCM of (12, 18) = 36 units. A's efficiency = 3, B's efficiency = 2. Combined = 5. In 6 days, they finish 5 × 6 = 30 units. Left = 36 - 30 = 6 units. Fraction left = 6/36 = 1/6.

⚠️ Common Student Trap / Pitfall

Many students calculate the work done (30/36 = 5/6) and mark it as the answer, forgetting the question asks for the work 'left to be done'.

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Calculate Total Work

Assuming total work is the Least Common Multiple (LCM) of 12 and 18, which is 36 units.

Total Work=36units\text{Total Work} = 36 unitsTotal Work=36units

Determine Individual Efficiencies

Efficiency is Work/Time. A's efficiency = 36/12 = 3 units/day. B's efficiency = 36/18 = 2 units/day.

(A+B)eff=3+2=5units/day(A+B)_{eff} = 3 + 2 = 5 units/day(A+B)eff​=3+2=5units/day

Calculate Work Completed

In 6 days of working together, total work completed is 6 days multiplied by combined efficiency.

Workdone=5×6=30unitsWork_{done} = 5 \times 6 = 30 unitsWorkdone​=5×6=30units

Calculate Remaining Work

Subtract the completed work from total units and find the fraction of the job left.

Workleft=36−3036=636=16Work_{left} = \frac{36 - 30}{36} = \frac{6}{36} = \frac{1}{6}Workleft​=3636−30​=366​=61​

✅

D is correct because 30 out of 36 units of work were completed, leaving 6 units, which is 1/6 of the total job.

Core Concepts Used

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Work and Time LCM Efficiency Method Fractional Work Calculation

💡 EXAM TIP

This LCM efficiency technique is identical to calculating the combined pipe fill rate in Pipe and Cistern problems.

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