The price of sugar has risen by 20%. By how much per cent must a house

1.	The price of sugar has risen by 20%. By how much per cent must a housewife reduce her consumptionofsugar, so as not to increase her expenditure on it?
Answer» Price × consumption = constant initial price = pchanged price = p' = 1.2pinitial consumption= Cchanged consumption= c' p'c' = pc 1.2p × c' = pc c' = pc/1.2p c' = c/1.2 = 0.83c Reduction in consumption is 17% I cant understand Right answer is Let the original Price of Sugar = x Rs/kg Let The Original Consumption = y Kgs Hence Original Expenditure = Rs. (xy) New Price = x + (20/100)x = 1.2x Let the new consumption = z New Expenditure = 1.2xz But according to question xy = 1.2xz ⇒ y = 1.2z ⇒ z = y/1.2 = (5y/6) Let the Percentage Decrease in Consumption = p y - (p/100)y = 5y/6 ⇒ 1 - (p/100) = 5/6 ⇒ 1/6 = p/100 ⇒ p = 100 / 6 = 50 / 3 = 16.66%

The price of sugar has risen by 20%. By how much per cent must a housewife reduce her consumptionofsugar, so as not to increase her expenditure on it?

Answer»

Price × consumption = constant

initial price = pchanged price = p' = 1.2pinitial consumption= Cchanged consumption= c'

p'c' = pc

1.2p × c' = pc

c' = pc/1.2p

c' = c/1.2 = 0.83c

Reduction in consumption is 17%

I cant understand

Right answer is

Let the original Price of Sugar = x Rs/kg

Let The Original Consumption = y Kgs

Hence Original Expenditure = Rs. (xy)

New Price = x + (20/100)x = 1.2x

Let the new consumption = z

New Expenditure = 1.2xz

But according to question

xy = 1.2xz

⇒ y = 1.2z

⇒ z = y/1.2 = (5y/6)

Let the Percentage Decrease in Consumption = p

y - (p/100)y = 5y/6

⇒ 1 - (p/100) = 5/6

⇒ 1/6 = p/100

⇒ p = 100 / 6 = 50 / 3 = 16.66%