the price elasticity of demand of good X is double the price elasticity of demand of good Y.a 10℅ rise no the price of good Y results in fall in it's demand by 60 units. if original demand of commodity Y was 400,calculate percentage rise in quantity demanded of good X when its price falls from Rs 10to Rs8 per unit

According to the question :
Ed of X = 2Ed of Y

% change in price of Y = 10
📐Q of Y= (-60)
Q of Y = 400 Q1 of Y = 340

P of X = 10 P1 of X = 8

and we need to find
% change in demand of X = ?

now from the given information we can calculate

📐P of X = P1 of X - P of X
= 8 -10
= ( -2 )

% change in demand of Y
= 📐Q of Y/Q of Y * 100
= (-60 )/400 * 100
= (-15)

now as we know % change in price and demand of Y we can calculate it's Ed

Ed of Y = % change in demand of Y / % change in price of Y
= (-15)/10
= (-1.5)

now in the question we had the information that

Ed of X = 2Ed of Y
Ed of X = 2*(-1.5)
= (-3)

now % change in price of X
= 📐P of X/ P of X * 100
= ( - 2)/10 * 100
= (-20)

Ed of X = % change in demand of X/ % change in price of X

(-3) = % change in demand of X / (-20)

NOW FINALLY
% change in demand of X = 60 %

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