CAT 2023 Set-1 | Quantitative Aptitude | Question: 14

Question

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

Answer 1

Let the amount of work they can do per day be $\frac{1}{a-d},\frac{1}{a}, \frac{1}{a+d} $

Now it is given that Kamal takes twice as much time as Amal to do the same amount of job, this means

$2*\frac{1}{a+d}=\frac{1}{a-d}$, which gives us $a=3d$ , the amount of the work done by them can be rewritten as $\frac{1}{2d},\frac{1}{3a}, \frac{1}{4d} $

If Amal and Sunil work for $4$ days and  $9$ days, respectively, Kamal needs to work for $16$ days to finish the remaining job.

can be written as $\frac{4}{2d} + \frac{9}{3d} +\frac{16}{4d} =$ Some work. 

Let the number of days taken by Sunil to complete the work be $t$, then

$t*\frac{1}{3d} = \frac{4}{2d} + \frac{9}{3d} +\frac{16}{4d} $ , we can take $d$ as common and remove it and after solving we will get $t=27$

 

Hence answer is $27\space days$