Question

the sum of two numbers is 1000. If the larger one is decreased by 10% and the smaller one is increased by 20% then the sum is decreased by 3.4% . The larger number is ?

Answer 1

The larger no. is 780 and smaller is 220 
Sol . let the two number be x and y
Given x+y = 1000...................(i)

Also given 0.9x+1.2y= 1000(96.6/100)
                    9x+12y=9660 ...................(ii)

Multiply (i) by 9 and subtract from (ii)

Solve
9x+12y=9660
9x+9y=9000
-------------------
      3y=660
        y=220

Therefore y ⇒220 and x⇒ 1000-220 ⇒780