CAT Quantitative Aptitude Questions | CAT Time and Work questions

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The question is from Time and Work: Making toys. Some details are given about A, B and C's efficiency. We need to find out A's efficiency to determine how many days he would take to complete 256 toys? Interesting Time and Work Question.

Question 23: A, B and C are to make 100 toys. In a day, they can together make 25 toys. A starts to work alone and makes 32 toys in some days. A then leaves and B and C works to make the remaining toys. It takes 8 days overall to make the 100 toys. How many days will it take for A to make 256 toys alone?

  1. 16 days
  2. 32 days
  3. 64 days
  4. 30 days

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Explanatory Answer

Method of solving this CAT Question from Pipes Cisterns and Work Time: How many days A took to complete 32 toys?

A, B and C together could make 100 toys in \\frac{100}{25}\\) = 4 days
i.e. A + B + C => 4 days
Total time taken when first A worked then B + C worked -> 8 days (i.e. 2 x 4)
Hence, it is as if A and (B+C) worked alternatively for 4 days each to complete the 100 days
So, A can make 32 toys in 4 days => In a day, A can make = \\frac{32}{4}\\) = 8 toys/day
To make 256 toys, A will take = \\frac{256}{8}\\) = 32 days

The question is "How many days will it take for A to make 256 toys alone?"

Hence, the answer is "32 days".

Choice B is the correct answer.

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