If increasing 30 by P% gives the same result as decreasing 90 by P% , what is the value of P ?
Let the result in both cases be R. Then,
(1 + P/100)*30 = R (increasing 30 by P%)
(1 - P/100)*90 = R (decreasing 90 by P%)
Subtracting the 2nd eqn from the 1st eqn,
(30 + (3/10)P) - (90 - (9/10)P) = 0
(30 - 90) + (3/10 + 9/10)P = 0
-60 + (12/10)P = 0
6P/5 = 60
P = 50
Check
(increasing 30 by 50%) 30 + 15 = 45
(decreasing 90 by 50%) 90 - 45 = 45