The rate of water flow through three pipes A, B and C are in the ratio 4 : 9 : 36. An empty tank can be filled up completely by pipe A in 15 hours. If all the three pipes are used simultaneously to fill up this empty tank, the time, in minutes, required to fill up the entire tank completely is nearest to

✅ Correct Option: 3

The flow rates of pipes A, B and C are in the ratio $4 : 9 : 36$ , and pipe A alone fills the tank in $15$ hours.

Since pipe A fills the tank in $15$ hours, its rate is

$\dfrac{1}{15}$ tank per hour

Pipe A corresponds to $4$ parts in the ratio, so

$4 \text{ parts} = \dfrac{1}{15}$

$1 \text{ part} = \dfrac{1}{60}$

Using this, we get the individual rates:

Pipe	Ratio Parts	Rate (tank/hour)
A	4	$\dfrac{4}{60}$
B	9	$\dfrac{9}{60}$
C	36	$\dfrac{36}{60}$

When all three pipes work together, their rates add up:

$\text{Combined Rate} = \dfrac{4}{60} + \dfrac{9}{60} + \dfrac{36}{60} = \dfrac{49}{60}$ tank per hour

Time to fill the tank is the reciprocal of the combined rate (since Time $= \dfrac{1}{\text{Rate}}$ ):

$\text{Time} = \dfrac{1}{\frac{49}{60}} = \dfrac{60}{49}$ hours

Converting to minutes:

$\dfrac{60}{49} \times 60 = \dfrac{3600}{49} \approx 73.47$ minutes

$\boxed{\approx 73 \text{ minutes}}$

CAT 2020 Slot 3

A contractor agreed to construct a $6$ km road in $200$ days. He employed $140$ persons for the work. After $60$ days, he realized that only $1.5$ km road has been completed. How many additional people would he need to employ in order to finish the work exactly on time?

CAT 2021 Slot 3

One day, Rahul started a work at $9$ AM and Gautam joined him two hours later. They then worked together and completed the work at $5$ PM the same day. If both had started at $9$ AM and worked together, the work would have been completed $30$ minutes earlier. Working alone, the time Rahul would have taken, in hours, to complete the work is

CAT 2019 Slot 1

At their usual efficiency levels, $A$ and $B$ together finish a task in $12$ days. If $A$ had worked half as efficiently as she usually does, and $B$ had worked thrice as efficiently as he usually does, the task would have been completed in $9$ days. How many days would $A$ take to finish the task if she works alone at her usual efficiency?

2025 Slot 1

Arun, Varun and Tarun, if working alone, can complete a task in 24, 21, and 15 days, respectively. They charge Rs 2160, Rs 2400, and Rs 2160 per day, respectively, even if they are employed for a partial day. On any given day, any of the workers may or may not be employed to work. If the task needs to be completed in 10 days or less, then the minimum possible amount, in rupees, required to be paid for the entire task is

CAT 2017 Slot 2

Amal can complete a job in $10$ days and Bimal can complete it in $8$ days. Amal, Bimal and Kamal together complete the job in $4$ days and are paid a total amount of Rs $1000$ as remuneration. If this amount is shared by them in proportion to their work, then Kamal's share, in rupees, is

CAT 2018 Slot 2

A water tank has inlets of two types $A$ and $B$ . All inlets of type $A$ when open, bring in water at the same rate. All inlets of type $B$ , when open, bring in water at the same rate. The empty tank is completely filled in $30$ minutes if $10$ inlets of type $A$ and $45$ inlets of type $B$ are open, and in $1$ hour if $8$ inlets of type $A$ and $18$ inlets of type $B$ are open. In how many minutes will the empty tank get completely filled if $7$ inlets of type $A$ and $27$ inlets of type $B$ are open?

Solution

Related questions:

Keyboard Shortcuts

CAT Past Year Questions (Topic-Wise)