# CAT Practice : Pipes cisterns, Work time

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Classic Work - Time Question!!

## Iphone 16s

Q.25: It’s year 2025 and iphone16 has just been launched. Apple has claimed that it is the best iphone they have created so far. It’s 4 charging inlets have completely revolutionized the mobile market. If only top and bottom inlets are used, it takes 20 mins to fully charge. If the right, left and bottom inlet are used, it takes 15 mins to fully charge. If top, left and right inlets are used, it takes 12 mins to charge.. What is the fastest possible time in which the iphone16 can be fully charged?
1. 12 min
2. 8 min
3. 11 min
4. 10 min

Choice D. 10 min

## Detailed Solution

Obviously, if all the 4 inlets are used, the iphone will be recharged in the fastest possible time.

Let, Time taken by Top, Left, Right and Bottom inlet to individually charge the phone be represented by A, B, C, and D respectively.

Given,

$\frac{1}{A} + \frac{1}{D} = \frac{1}{20}$

$\frac{1}{B} + \frac{1}{C} + \frac{1}{D} = \frac{1}{15}$

$\frac{1}{A} + \frac{1}{B} + \frac{1}{C} = \frac{1}{12}$

=) $2 * (\frac{1}{A} + \frac{1}{B} + \frac{1}{C} + \frac{1}{D}) = \frac{1}{12} + \frac{1}{15} + \frac{1}{12} = \frac{(15+20+25)}{300} = \frac{1}{5}$

=) $\frac{1}{A} + \frac{1}{B} + \frac{1}{C} + \frac{1}{D} = \frac{1}{10}$

Therefore, all 4 together will take 10 minutes to fully charge the iphone.

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## More questions from Pipes Cisterns, Work Time

Mathematicians are creatures of habit. This topic has been called Pipes and Cisterns because someone named it like it long ago. Pipes and Tanks would be much better - at least makes it sound like wartime.