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Profit/Loss Per cent
The percentage of profit or loss is always calculated on the cost price.
Profit (gain) % = Profit × 100% And Loss % = Loss × 100%
CP CP
Example 6: Lalan bought a second-hand motorcycle for
`20,500, then spent `4,500 on its repairs and sold it for Think and Answer
`30,000. Find his loss or gain per cent.
Madhu: For the school fair (mela),
Solution: Cost Price (CP) = `20,500 + `4,500 = `25,000 I am going to put up a stall of lucky
(overhead expenses are added to CP) dips. I will charge `20 for one lucky
dip, but I will put items that are
Selling Price (SP) = `30,000 worth `10.
Since, SP > CP Vijay: So you are making a profit
10
Therefore, he made a profit = `30,000 – `25,000 = `5,000 of 20 × 100% = 50%.
Profit Madhu: No, I will spend `5 on paper
So, Profit % = × 100% to wrap the gift and tape. So, my
CP expenditure is `15. This way, I will
5000
= × 100% = 20% 5 1
25000 gain 15 × 100% = 33 % only.
3
Example 7: If the CP of 10 bananas is equal to the SP of 12
bananas, find the profit or loss per cent in this deal.
Solution: Let the CP of 1 banana = `1
So, CP of 12 bananas = `12
Since, SP of 12 bananas = CP of 10 bananas = `10
Since, SP < CP, so it is a loss. 1. What do you think about the
calculation done by Vijay?
Loss = CP – SP = `12 – `10 = `2
2. Recognise overhead expenses.
Loss What is Madhu’s actual profit:
Loss % = × 100%
1
CP 25% or 33 %?
2 2 3
= × 100% = 16 %
12 3
Finding SP/CP when Profit/Loss Per cent is Given
When profit % or loss % is given, then to calculate the selling price (SP) or the cost price (CP), we
use the following formulae:
If the profit % (P%) is given, then
100
SP = 100 + P% × CP and CP = 100 + P% × SP
100
If the loss % (L%) is given, then
100
SP = 100 − L% × CP and CP = 100 − L% × SP
100
171 Comparing Quantities
