Chain Rule Q35

35. A garrison had provisions for a certain number of days. After 10 days,

1/5 of the men desert and it is found that the provisions will now last

just as long as before. How long was that?

Answer:

        Let initially there be x men having food for y days.

              After, 10 days x men had food for ( y-10)days

              Also, (x -x/5) men had food for y days.

              x(y-10)=(4x/5)*y

            => (x*y) -50x=(4(x*y)/5)

              5(x*y)-4(x*y)=50x

                x*y=50x

                  y=50