If increasing 30 by P% gives the same result as decreasing 90 by P% , what is the value of P ?

Question

This is a Percentage Word Problem Question.we can solve by percent increasing method and percent decreasing method.

Answer 1

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