The price of 2 sarees and 4 shirts is Rs. 1600. With the same money one can buy 1 saree and 6 shirts. If one wants to buy 12 shirts, how much shall he have to pay ?

Solution(By Examveda Team)

$$\eqalign{ & {\text{Let}}\,{\text{the}}\,{\text{price}}\,{\text{of a}}\,{\text{saree}}\,{\text{and}}\,{\text{a}}\,{\text{shirt}} \cr & \,{\text{be}}\,Rs.\,x\,{\text{and}}\,Rs.\,y\,{\text{respectively}}. \cr & {\text{Then,}}\,2x + 4y = 1600\,....(i) \cr & \,\,\,\,\,\,\,\,\,\,\,{\text{and}}\,x + 6y = 1600\,....(ii) \cr & {\text{Divide}}\,{\text{equation}}\,(i)\,by\,2, \cr & {\text{we}}\,{\text{get}}\,{\text{the}}\,{\text{below}}\,{\text{equation}}. \cr & = > \,x + 2y = 800\,\, - - - (iii) \cr & {\text{Now}}\,{\text{subtract}}\,(iii)\,{\text{from}}\,(ii) \cr & x\,\, + \,\,\,\,6y\,\, = \,\,1600\,\,\,( - ) \cr & x\,\, + \,\,\,\,2y\,\, = \,\,\,\,\,\,\,800 \cr & - - - - - - - - - - \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,4y\,\, = \,\,\,\,\,\,800 \cr & - - - - - - - - - - \cr & {\text{Therefore}},\,y = 200 \cr & {\text{Nowapply}}\,{\text{value}}\,{\text{of}}\,y\,{\text{in}}\,(iii) \cr & = > x + 2 \times 200 = 800 \cr & = > x + 400 = 800 \cr & {\text{Therefore}}\,x = 400 \cr & {\text{Solving}}\,(i)\,{\text{and}}\,(ii)\,{\text{we}}\,{\text{get}}\, \cr & x = 400,\,y = 200 \cr & \therefore {\text{Cost}}\,{\text{of}}\,{\text{12}}\,{\text{shirts}} \cr & = Rs.\,\left( {12 \times 200} \right) \cr & = Rs.\,2400 \cr} $$