FORTNIGHT'S PUZZLE 7

PUZZLE 7: 11th-17th January (to be e-mailed by the 18th January)
POSTED BY IES CAMPANAR

A FIERCE BATTLE
In a fierce battle, say that at least 70% of the soldiers have lost an eye; at least 75% an ear; at least 80% an arm; and at least 85% a leg.What percentage, at least, must have lost all four? (Lewis Carroll)

SOLUTION
At least 45% lost an eye and an ear (70+75 = 145)At least 65% lost an arm and a leg ( 80 +85 = 165)Therefore at least 10% lost an eye, an ear, an arm and a leg (45 + 65 = 110).