CBSE Class 10 Mathematics Profit, Loss and Discount Notes Set 13

Cost Price, Selling Price, Profit and Loss

Cost price (CP) is what the seller pays and selling price (SP) is what the buyer pays. If SP is more than CP the seller has a profit equal to SP − CP; if SP is less than CP there is a loss equal to CP − SP.
Profit % = (Profit/CP) × 100 and Loss % = (Loss/CP) × 100. Both percentages are always calculated on the cost price unless the question says otherwise.
SP = CP × (100 + profit %)/100 for a profit and SP = CP × (100 − loss %)/100 for a loss. Reverse these to find CP from SP: CP = SP × 100/(100 + profit %) or SP × 100/(100 − loss %).

Marked Price and Discount

The marked (list) price is the price printed on the article. A discount is a reduction on the marked price, so Discount % = (Discount/Marked price) × 100 and SP = MP − discount = MP × (100 − d)/100.
A mark-up is calculated on the cost price: MP = CP × (100 + mark-up %)/100. Remember that mark-up is on CP but discount is on MP.
Two successive discounts of a% and b% are equivalent to a single discount of a + b − ab/100 percent, because the factors multiply: (1 − a/100)(1 − b/100).

Useful Short Cuts

If CP of x articles equals SP of y articles, the profit % is (x − y)/y × 100.
If two articles are sold at the same price, one at a gain of p% and the other at a loss of p%, there is always a loss of p²/100 percent.
A dishonest shopkeeper who sells at cost price but uses a false weight gains (true weight − false weight)/false weight × 100 percent.
If a part of the stock is sold at different profit rates, the overall profit % is the weighted average of the rates by the share of stock (or cost) sold at each rate.

Worked Examples

Illustration 1. A shopkeeper marks an article 40% above cost and allows a discount of 10%. Find his profit percent.
Answer:
Take CP = 100, so MP = 140 and SP = 140 × 0.9 = 126.
Answer: profit = 26%.

Illustration 2. By selling a watch for Rs. 1140 a man loses 5%. At what price should he sell it to gain 5%?
Answer:
CP = 1140 × 100/95 = Rs. 1200.
SP for a 5% gain = 1200 × 1.05 = Rs. 1260.

Illustration 3. Two successive discounts of 20% and 10% are given. Find the single equivalent discount.
Answer:
Equivalent discount = 20 + 10 − (20 × 10)/100 = 28%.