If 6 men and 8 boys can do a piece of work in 10 days while 26 men and 48 boys can do the same in 2 days, the time taken by 15 men and 20 boys in doing the same type of work will be:

Solution (By Examveda Team)

$$\eqalign{ & {\text{Let}}\,{\text{1}}\,{\text{man's}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} = x\,{\text{and}} \cr & 1\,{\text{boy's}}\,{\text{1day's}}\,{\text{work}} = y \cr & {\text{Then,}}\,6x + 8y = \frac{1}{{10}}\,{\text{and}}\, \cr & 26x + 48y = \frac{1}{2} \cr & {\text{Solving}}\,{\text{these}}\,{\text{two}}\,{\text{equations,}}\,{\text{we}}\,{\text{get}} \cr & x = \frac{1}{{100}}\,and\,y = \frac{1}{{200}} \cr & {\text{(15}}\,{\text{men}}\,{\text{ + 20}}\,{\text{boy)'s}}\,{\text{1}}\,{\text{day's}}\,{\text{work}} \cr & = {\frac{{15}}{{100}} + \frac{{20}}{{200}}} = \frac{1}{4} \cr & \therefore {\text{15}}\,{\text{men}}\,{\text{and}}\,{\text{20}}\,{\text{boys}}\,{\text{can}}\,{\text{do}}\,{\text{the}}\,{\text{work}}\,{\text{in}}\,{\text{4}}\,{\text{days}} \cr} $$