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CAT 2018 Slot 2 — QA Question 9

Pipes & CisternsEasy

A tank is emptied everyday at a fixed time point. Immediately thereafter, either pump A or pump B or both start working until the tank is full. On Monday, A alone completed filling the tank at 8 pm. On Tuesday, B alone completed filling the tank at 6 pm. On Wednesday, A alone worked till 5 pm, and then B worked alone from 5 pm to 7 pm, to fill the tank. At what time was the tank filled on Thursday if both pumps were used simultaneously all along?

Answer & solution

  • A

    4:36 pm

  • B

    4:12 pm

  • C

    4:48 pm

  • 4:24 pm

Solution

Easy

Let A alone take tt hours and B alone take t−2t-2 hours (B finishes 22 h earlier on Tue than A on Mon, both starting at the same emptying time). Wednesday's split (A for some hours, then B for 22 h) gives the efficiency ratio; combine to solve for tt and the start time, then find the both-pumps finish time.

1

Relate the alone-times. The tank empties at the same fixed time each day. A alone finishes at 88 pm (Mon), B alone at 66 pm (Tue) — so B is 22 hours faster than A.

tB=tA−2(let tA=t)\begin{aligned} &t_B = t_A - 2 \quad\text{(let }t_A=t\text{)} \end{aligned}
2

Wednesday gives the efficiency ratio. A worked till 55 pm; alone A would have run till 88 pm, so A worked 33 hours short. B then worked 55–77 pm =2=2 hours and finished. So B's 22 hours did the work A's missing 33 hours would have done.

3⋅eA=2⋅eB(equal work)⇒ eA:eB=2:3\begin{aligned} &3\cdot e_A = 2\cdot e_B \quad\text{(equal work)}\\ &\Rightarrow\ e_A:e_B = 2:3 \end{aligned}

Write eA=2x, eB=3xe_A=2x,\ e_B=3x.

3

Solve for tt via total work. Total work =eA⋅t=eB⋅(t−2)=e_A\cdot t = e_B\cdot(t-2).

2x⋅t=3x⋅(t−2)⇒ 2t=3t−6⇒ t=6 hours\begin{aligned} &2x\cdot t = 3x\cdot (t-2)\\ &\Rightarrow\ 2t = 3t-6\\ &\Rightarrow\ t = 6\ \text{hours} \end{aligned}

So A takes 66 h and finishes at 88 pm ⇒\Rightarrow the tank starts filling at 22 pm.

4

Both pumps together. Total work =eA⋅t=2x⋅6=12x=e_A\cdot t = 2x\cdot 6 = 12x. Combined rate =eA+eB=5x=e_A+e_B=5x.

tboth=12x5x=2.4 h=2 h 24 min\begin{aligned} &t_{\text{both}} = \frac{12x}{5x} = 2.4\ \text{h} = 2\ \text{h }24\ \text{min} \end{aligned}

Starting at 22 pm: 2:00+2:24=4:242{:}00 + 2{:}24 = 4{:}24 pm.

Filled at 4:24 pm(option d)\text{Filled at } 4{:}24\ \text{pm}\quad\text{(option d)}
CAT 2018 Slot 2 QA Q9: A tank is emptied everyday at a fixed time point. Immediately thereafter, either pump A or pump B or both star — Solution | TheCATExam