Question

To keep the product of 2 numbers same, If one is increased by 40% then by what % will the $2^{nd}$ be decreased

Answer 1

Let the two numbers be X and Y.
product = XY
let X is decreased by 40%
40% of X = (40/100)× X = 40X/100 = 0.4X
by reducing X by 40%, it becomes x
x = X - 0.4X = 0.6X

Let Y becomes y after increasing.
xy = XY
⇒ 0.6X × y = XY
⇒ y = XY/0.6X
⇒ y = Y/0.6 = 10Y/6 
⇒y = = 5Y/3

% increase = $\frac{ \frac{5Y}{3} -Y}{Y} *100= \frac{ \frac{5Y-3Y}{3} }{Y} *100= \frac{2Y}{3Y} *100= \frac{100*2}{3} =66.7$%