NinetynineCAT 2023 Slot 1 QA Q15 Time & Work
Question 15 of the Quantitative Ability (QA) section, CAT 2023 Slot 1, with CAT's official answer and a worked solution.
The amount of job that Amal, Sunil and Kamal can individually do in a day, are in harmonic progression. Kamal takes twice as much time as Amal to do the same amount of job. If Amal and Sunil work for 4 days and 9 days, respectively, Kamal needs to work for 16 days to finish the remaining job. Then the number of days Sunil will take to finish the job working alone, is
TITA: type in the answer. There are no options and no negative marking.
Answer: 27 Time & Work TITA
Solution
- Let daily work be \(a, s, k\) (in HP). Kamal takes twice Amal's time, so \(k = \frac a2\).
- The reciprocals \(\frac1a, \frac1s, \frac2a\) are in AP: \(\frac2s = \frac3a\), so \(s = \frac{2a}{3}\).
- Total job \(= 4a + 9s + 16k = 4a + 6a + 8a = 18a\).
- Sunil alone needs \(\frac{18a}{2a/3} = 27\) days.