Exams › IBPS PO › Quantitative Aptitude

Directions: In the following question, two statements are numbered as Quantity I and Quantity II. Solve both quantities and choose the correct option. Quantity I: Pipe A can fill a tank in 3 hours, Pipe B can fill the same tank in 4 hours, and Pipe C can fill the same tank in 5 hours. What is the time taken when all of them work together? Quantity II: Two pipes A and B can fill a tank in 8 hours. Pipe C can fill the same tank in 10 hours. Pipes C and D fill the tank in 15 hours. Pipe D can fill the same tank in 30 hours. Find the time taken by them to fill the tank together.

1. Quantity I > Quantity II
2. Quantity I < Quantity II
3. Quantity I = Quantity II
4. Quantity I ≤ Quantity II

Correct answer: Quantity I < Quantity II

Solution

Quantity I has rate $\frac{1}{3}+\frac{1}{4}+\frac{1}{5}=\frac{47}{60}$ tank/hour, so time is $\frac{60}{47}$ hours. In Quantity II, from A+B=1/8 and C=1/10, C+D=1/15, D=1/30, we get D=1/30 and C=1/15, so A+B=1/8 and total rate = 1/8 + 1/15 + 1/30 = 19/120, giving time $\frac{120}{19}$ hours. Since $\frac{60}{47} < \frac{120}{19}$, Quantity I < Quantity II.

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