Profit and Loss 9

An article is sold for $ 480. Find its C.P. if it is sold at

(i) 20 % profit (ii) 20 % loss

Solution:

(i) Let C.P. = $ 100. Since, Profit = 20 % of $ 100 = $ 20

Therefore, S.P. = $ 100 + $ 20 = $ 120

When S.P. = $ 120, C.P. = $ 100

When S.P. $ 1, C.P. = $ 100 / 120

And, when S.P. = $ 480, C.P. = $ 100 / 120 X 480 = $ 400

(ii) Let C.P. = $ 100. Since, loss = 20 % of $ 100 = $ 20

Therefore, S.P. = $ 100 - $ 20 = $ 80

When S.P. = $ 80, C.P. = $ 100

When S.P. = $ 1, C.P. = $ 100 / 80

And, when S.P. = $ 480, C.P. = $ 100 / 80 X 480 = $ 600

Alternative Method:

In case of profit: C.P. = [100 / (100 + Profit %)] X S.P.

In case of loss: C.P. = [100 / (100 - Loss %)] X S.P.

(i) C.P. = [100 / (100 + 20)] X $ 480 = 100 / 120 X $ 480 = $ 400

(ii) C.P. = [100 / (100 - 20)] X $ 480 = 100 / 80 X 480 = $ 600

Algebraic Method:

(i) Let C.P. = $ x

Therefore, C.P. + Profit = S.P.

=> x + 20 % of x = $ 480

=> x + 20 X / 100 = $ 480

=> 6 x / 5 = $ 480

=> x = $ 5 / 6 X 480 = $ 400

i.e. C.P. = $ 400

(ii) Let C.P. = $ x

Therefore, C.P. - Loss = S.P.

=> x - 20 % of x = $ 480

=> x - 20 x / 100 = $ 480

=> 4 x / 5 = $ 480

=> x = $ 5 / 4 X 480 = $ 600

i.e. C.P. = $ 600