PROFIT AND LOSS – IMPORTANT FACTS
Cost Price:
The price, at which an article is purchased, is called its cost price, abbreviated as C.P.
Selling Price:
The price, at which an article is sold, is called its selling prices, abbreviated as S.P.
Profit or Gain:
If S.P. is greater than C.P., the seller is said to have a profit or gain.
Loss:
If S.P. is less than C.P., the seller is said to have incurred a loss.
IMPORTANT FORMULAE
1. Gain = (S.P.) – (C.P.)
2. Loss = (C.P.) – (S.P.)
3. Loss or gain is always reckoned on C.P.
4. Gain Percentage: (Gain %) Gain % = (Gain ×100)/(C.P.)
5. Loss Percentage: (Loss %) Loos % =(Loss ×100)/(C.P.)
6. Selling Price: (S.P.) SP = [((100+Gain%))/100×C.P.]
7. Selling Price: (S.P.) SP = [((100-Loss%))/100×C.P.]
8. Cost Price: (C.P.) C.P. = [100/((100-Gain%) )×S.P.]
9. Cost Price: (C.P.) C.P. = [100/((100-Loss%) )×S.P.]
10. If an article is sold at a gain of say 35%, then S.P. =135% of C.P.
11. If an article is sold at a loss of say, 35% then S.P. =65% of C.P.
12. When a person sells two similar items, one at a gain of say x%, and the other at a loss of x%, then the seller always incurs a loss given by:
Loss % =((Common loss andGain%)/10)^2 = (〖x/y)〗^2
13. If a trader professes to sell his goods at cost price, but uses false weights, then
Gain % = [Error/((True Value)-(Error) )×100]%
SOLVED EXAMPLES
- Ex.1: A man buys a toy for Rs 25 and sells it for Rs 30. Find his gain per cent.
Sol.: % Gain = Gain/CP×100=5/25 ×100=20% - Ex.2: If by selling an article for Rs 390 a shopkeeper gains 20%, find his cost.
Sol.: If the SP be Rs 120, the CP is Rs 100
If the SP be Rs 390, the CP is Rs 100/120×390= Rs 325. - Ex.3: Prasak sold his work tools for Rs. 1850 and earned a profit 25 per cent. At what price did Prasad by the work tools?
(1) Rs. 1,360 (2) Rs. 1,300 (3) Rs. 1,240
(4) Rs. 1,480 (5) None of these
Sol.: C.P. = 100/(100+Profit per cent) ×S.P.
=100/125×1850=Rs.1480 - Ex.4 Seema purchased an item for `9,600 and sold it for a loss of 5 percent. From that money she purchased another item and sold it for a gain of 5 percent. What is her overall gain/loss ?
(1) Loss of `36 (2) Profit of `24
(3) Loss of `54 (4) Profit of `36
(5) None of these
Sol.: First S.P. = (9600×95)/100 = 9120
= (9120×105)/100 = Rs. 9576
Second S.P. Rs. 9576
Loss = 9600 – 9576 = Rs. 24 - Ex.5 In a sale, a discount of 15% was available on all the articles. If Vinit purchased an article for Rs. 4,284 in the sale, what was the actual selling price
of the article?
(1) Rs. 5,050 (2) Rs. 5,000 (3) Rs. 5,140 (4) Rs. 4,950 (5) None of these
Sol.: Actual selling price
= Rs. (100/85×4284) = Rs. 5040
