Work and Time with Varied Efficiencies

CAT 2019 Slot 1 · QA · Medium · Work, time

All CAT 2019 Slot 1 questionsMore Work, time questionsAll CAT QA

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?

  1. A.

    18

  2. B.

    12

  3. C.

    24

  4. D.

    36

Answer

A

Explanation

Let work rate of A be aa and B be bb. 12(a+b)=1  ⟹  a+b=11212(a + b) = 1 \implies a + b = \frac{1}{12}. 9(a2+3b)=1  ⟹  a2+3b=199\left(\frac{a}{2} + 3b\right) = 1 \implies \frac{a}{2} + 3b = \frac{1}{9}. Multiply first equation by 3: 3a+3b=312=143a + 3b = \frac{3}{12} = \frac{1}{4}. Subtract second equation: 3a−a2=14−19  ⟹  5a2=536  ⟹  a=236=1183a - \frac{a}{2} = \frac{1}{4} - \frac{1}{9} \implies \frac{5a}{2} = \frac{5}{36} \implies a = \frac{2}{36} = \frac{1}{18}. Days taken by A alone =18= 18.

Practise this under exam conditions

Sign in to solve it with a live timer, the on-screen CAT calculator, and streak and accuracy tracking across every question you attempt.

Solve in the workspace