Xavier Aptitude Test 2020 Paper

Let the work done per day by $\mathrm{X}$, $\mathrm{Y}$ and $\mathrm{Z}$ is respectively $\mathit{x}$, $\mathit{y}$ and $\mathit{z}$ units.
According to the first statement, out of 6 days, $\mathrm{X}$ works for 5 days, and $\mathrm{Y}$ works for 5 days. Total work done $=5\mathit{x}+5\mathit{y}=1$
According to the second statement, out of 8 days, $\mathrm{Z}$ works for 7 days and $\mathrm{X}$ works for 6 days and they complete two jobs. $7\mathit{z}+6\mathit{x}=2$...
According to the third statement, out of 12 days, $\mathrm{Y}$ works for 10 days and $\mathrm{Z}$ works for 10 days and they complete three jobs. $10\mathit{y}+10\mathit{z}=3$
Solving, we get $\mathit{x}=\frac{1}{10},\mathit{y}=\frac{1}{10},\mathit{z}=\frac{2}{10}$.
⇒ every day, $\mathrm{X}$ does 10% of the job, $\mathrm{Y}$ does 10% of the job and $\mathrm{Z}$ does 20% of the job.
Together, every day they can do 40% of the job. Hence to complete 100% of the job, they will take $\frac{100}{40}=2.5\mathrm{days}$.