Work and Time for A and B

CAT 2019 Slot 1 · QA · Easy · Work and Time

All CAT 2019 Slot 1 questionsMore Work and Time questionsAll CAT QA

When they work alone, B needs 25% more time to finish a job than A does. They two finish the job in 13 days in the following manner: A works alone till half the job is done, then A and B work together for four days, and finally B works alone to complete the remaining 5% of the job. In how many days can B alone finish the entire job?

  1. A.

    16

  2. B.

    22

  3. C.

    20

  4. D.

    18

Answer

C

Explanation

Let efficiency of A = 5e5e, efficiency of B = 4e4e (since time ratio B:A = 5:4). Work done by A alone = 50%. Work done by B alone = 5%. So work done by A and B together in 4 days = 100%−50%−5%=45%100\% - 50\% - 5\% = 45\%. Work done in 4 days by A+B = 4×(5e+4e)=36e4 \times (5e + 4e) = 36e. So 36e=45% of Total Work⇒Total Work=80e36e = 45\% \text{ of Total Work} \Rightarrow \text{Total Work} = 80e. Time taken by B alone = 80e4e=20\frac{80e}{4e} = 20 days.

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