The money spent to purchase an article is cost price of the article, and the money received for selling an article is called selling price.
Profit = selling price – cost price
Loss = cost price – selling price
Profit or loss percent is always calculated on C.P unless it is required to calculate on S.P.
The price at which the article is marked is the marked price or listed price or labeled price or catalogue price.
The discount is allowed on marked price for the cash payments.
When discount is deducted from the marked price, the remainder becomes the selling price.
To find Marked price from Cost Price we can use the following formula
Example 1. Ram sold a cow for Rs.136 at a loss of 15%. At what price should he have sold it to gain 15%?
Sol: Let the cost price be Rs.100 then for 15% loss the S.P = 85 and for 15% profit it should be Rs. 115.
Rs. 85 is the first S.P, then second S.P. = Rs. 115
Rs. 136 is the first S.P = 115*136/85
Example 2. A sells a radio to B at a gain of 10% and B sells it to C at a gain of 5%.If C pays Rs. 462 for it, What did it cost to A?
Sol: Let the cost price of A be Rs. 100
Then the cost price of B be Rs. 110
Example 3. A dealer allows 10% discount on the list price of a certain article and yet makes a profit of Rs. 25% on each article. Find the cost price of the article when list price is Rs. 50.
Sol: Let the cost price of articles be Rs. 100
Then for 25% profit, S.P. = Rs. 125
If list price is Rs. 100, S.P. = Rs. 90
If S.P. is Rs. 90, list price = Rs. 100
Example 4. A person purchases 90 clocks and sells 40 clocks at a gain of 10% and 50 clocks at a gain of 20%. Had he sold all of them at a uniform profit of 15% he would have got Rs.40 less. Find the cost price of each clock.
Sol: Let the C.P of clock is Rs. 100 each.
By the profit of 10% S.P. of 40 clocks = = Rs. 4, 400
By the profit of 20% S.P of 50 clocks = = Rs. 6, 000
Total S.P. = Rs. 4400 + Rs. 6, 000 = Rs. 10, 400
C.P of 90 clocks = = Rs. 9000
By the profit of 15% S.P. of 90 clocks = = Rs. 10, 350
Difference = Rs. 10, 400 – Rs. 10, 350 = Rs. 50
If the difference is Rs. 50 then C.P. = Rs. 100
If the difference is Rs. 40 then C.P. = 100*40/50 = Rs. 80
Example 5. A man buys 5 horses and 10 cows for Rs. 1,600. He sells horses at a profit of 15% and cows at a Loss of 10% if his over all profit was Rs. 90, what was the cost price of a horse and a cow?
Sol: Let x be the cost price of a horse and y be the cost price of a cow
∵ C.P. of 5 horses = Rs. 5x and C.P of 10 cows = Rs. 10y
Hence 5x + 10y = 1,600……..(i)
Since the profit is 15% on the horses