# maths -profit and loss

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The profit on a certain item is 20%. If the CP is increased by Rs 50 and SP is increased by Rs 30 then the profit 5 reduces by 3 1/3%. Find the original CP and SP.

• maths -profit and loss -

original case:
let CP = x

SP = 1.2x
profit = .2x

new SP = 1.2x + 30
new CP = x+50
new profit = 1.2x + 30 - (x+50)
= .2x - 20

but this new profit is 3 1/3% less than the old one
or it is 29/30 of the old one

.2x-20 = (29/30)(.2x)
6x - 600 = 5.8x
.2x = 600
x = 3000

original CP = 3000
original SP = 3600

check:
old CP = 3000
old SP = 3600
old profit = 600

new CP = 3050
new SP = 3600 + 30 = 3630
new profit = 580

change in profit = 20
percentage change in profit = 20/600 = .0333333 = 3 1/3%

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