If the price of gold increases by 30%, find by how much the quantity of ornaments must be reduced so that the expenditure may remain the same as before.

The price of gold increases by 30%

let the initial price be x

let the initial consumption by y

since the price of gold increases by 30 %

final price of gold =1.3x

now, expenditure=price*consumption

let the final consumption be z

given total expenditure remains constant

Therefore

x*y=1.3 x *z

Therefore z=(y/1.3)

% decrease=((initial consumption-final consumption)/initial consumption)*100%

Therefore,

 % decrease=((y-z)/y)*100%=(1-(1/1.3))*100%=(1-0.769)*100%=

= 23 1/13%