One pipe can fill the tank in 18 min, while another pipe can e... | Mathematics MCQ | Examoogle

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MathematicsTime and Work

One pipe can fill the tank in 18 min, while another pipe can empty the completely filled tank in 72 min. If both the pipes are operated together on empty tank, how long (in min) will it take to fill two-third of the tank? 3938

Correct Answer

📐 MA • Math LCM Efficiency MethodMathematicsTime and Work

Option B

Quick Summary:

Use the formula $T = \frac{xy}{y-x}$ to find time to fill, then multiply by the required fraction ( $2/3$ ). For $x=18, y=72$ , time for full tank is $24$ min; $2/3$ of $24 = 16$ .

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📐MAMath SolutionLCM Efficiency Method

📋 Given

Pipe A fills in 18 min, Pipe B empties in 72 min.

🔢 Formula Used

T=WEfficiencynetT = \frac{W}{\text{Efficiency}_{net}}T=Efficiencynet​W​

⚡ Exam Hall Shortcut / Speed Trick

Use the formula $T = \frac{xy}{y-x}$ to find time to fill, then multiply by the required fraction ( $2/3$ ). For $x=18, y=72$ , time for full tank is $24$ min; $2/3$ of $24 = 16$ .

⚠️ Common Student Trap / Pitfall

Students often calculate the time for a full tank (24 minutes) and forget to multiply by the fraction $2/3$ required by the question.

📊 Diagram / Illustration

🔢 Step-by-Step Solution

Calculate Net Efficiency

Assuming total capacity is the LCM of 18 and 72, which is $72$ units. Efficiency of Pipe A = $72 / 18 = 4$ units/min. Efficiency of Pipe B = $72 / 72 = -1$ unit/min (emptying). Net efficiency = $4 - 1 = 3$ units/min.

Enet=4−1=3 units/minE_{net} = 4 - 1 = 3 \text{ units/min}Enet​=4−1=3 units/min

Calculate Time for Full Tank

Time taken to fill the entire tank is total work divided by net efficiency.

Tfull=723=24 minT_{full} = \frac{72}{3} = 24 \text{ min}Tfull​=372​=24 min

Calculate Time for Two-Third Tank

Since the question asks for the time to fill only two-thirds of the tank, multiply $T_{full}$ by $2/3$ .

T2/3=24×23=16 minT_{2/3} = 24 \times \frac{2}{3} = 16 \text{ min}T2/3​=24×32​=16 min

✅

B is correct because the net efficiency is 3 units/min, leading to a full-tank time of 24 min, and 2/3 of 24 is 16 min.

Core Concepts Used

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Work and Time Efficiency LCM Method

💡 EXAM TIP

This concept is identical to solving questions involving 'relative speed' in distance-time problems, where you subtract speeds when objects move in opposite directions (one filling vs one emptying).

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