A person X can complete 20% of work in 8 days and another person Y can complete 25% of the same work in 6 days. If they work together, in how many days will 40% of the work be completed?

Correct Answer: (A) 6

Person X finishes 20% (1/5) in 8 days, so X completes the full work in $8$$\times$ 5 = 40 $\text{ days}$ (rate $1/40$). Person Y finishes 25% (1/4) in 6 days, so Y completes the full work in $6$$\times$ 4 = 24 $\text{ days}$ (rate $1/24$). Working together, their combined rate is $\frac{1}{40}+\frac{1}{24}=\frac{8}{120}=\frac{1}{15}$$\frac{1}{40}$ + $\frac{1}{24}$ = $\frac{8}{120}$ = $\frac{1}{15}$ per day. To complete 40% (2/5) of the work, the time required is $\frac{2\mathrm{/}5}{1\mathrm{/}15}=\frac{2}{5}\times 15=6\text{ days}$$\frac{2/5}{1/15}$ = $\frac{2}{5}$ $\times$ 15 = 6 $\text{ days}$.