CAT Quantitative Aptitude Questions | CAT Time and Work questions

The question is from Time and work: Charging Time. A future phone has multiple charge outlets, what would happen if we chose to use all the outlets? A unique Time and Work Question.

Question 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

Explanatory Answer

Method of solving this CAT Question from Pipes Cisterns and Work Time: Whoa, the future is here!

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}\\)
On adding all 3,
=> 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.

The question is "What is the fastest possible time in which the iphone16 can be fully charged?"

Hence, the answer is "10 min".

Choice D is the correct answer.