The chapter of profit and loss is a part & parcel of every commercial activity.

This chapter has a wide-ranging importance in exams. The concepts of application percentage rule, fraction to percentage change, are applicable to profit &loss.

**Cost Price :**The price at which an article is brought is called its cost price, abbreviated as C.P.

**Selling Price :**The price at which an article is sold is called its selling price, abbreviated as S.P.

**Profit or Gain**= (S.P.) - (C.P.)

**Loss**= (C.P.) - (S.P.)

Loss or Gain is always reckoned on C.P.

**Gain %**= Gain x

**Loss %**= Loss x

If Profit is P% If Loss is L%

**SP**= x CP SP = x CP

**CP**= x SP CP = x SP

**Value of Profit**= x CPValue of Loss = x CP

**Example 1: CP is 40% of SP. What is the % gain on CP?**

**Solution:**Let the SP = Rs. 100

CP = Rs. 40

Gain = (60/40) x 100% = 150%

**Example 2:**The loss when SP is Rs 27.8 is equal to the gain when SP is Rs 132.2. Find CP.

**Solution:**CP = = Rs. 80

**Example 3:**By selling 24 lemons the loss is equal to selling price of 8 lemons. Find the % Loss.

**Solution:**Let SP of 1 lemon = Rs. 1

Loss = x 100% = 25%

**Example 4:**By selling 24 lemons the gain is equal to the selling price of 8 lemons.

Find the gain %

**Solution:**Let SP of 1 lemon = Re. 1

Loss = x 100% = 50%

**Example 5:**A pretends to sell the goods at cost price but uses a weight of 960 g for 1 kg. Find his gain%.

**Solution:**Gain % = x 100 = 4.17 %

(Note: we use 960 because his cost is on Rs 960 and not on Rs 1000)

**Example 6:**A pretends to gain 20% but also uses a weight of 800 g for 1 kg. His actual gain is.

**Solution:**Let CP of 1 kg = Rs. 100

therefore, SP of 800 g = Rs. 120 (Sells it at 20% gain)

Gain = x 100%Therefore, Gain is 50%

**Example 7:**Selling price of two articles is Rs. 910 each. Gain on one is 30%. Loss on other is 30%. Find the final position.

**Solution:**CP of both = Rs. 910 x + Rs. 910 x = Rs. 2000

Therefore Loss = Rs. 2000 - 2. (Rs. 910) = Rs. 180

**Example 8:**Selling price of two articles is same. Gain on one is 20%. Loss on other 20%. On the whole the loss is ? %.

**Solution:**Loss = 20 x % = 4%, (If SP is same.)

**Example 9:**If SP is Rs. 48, loss is 37%. Find the SP to gain 26%.

**Solution:**New S. P = 126 % of CP

x = Rs. 96

**Example 10:**CP of 11 books = Rs. 5 SP of 10 books = Rs. 6. Find the gain percent.

**Solution:**Let the number of books = 110 (the LCM of 11 & 10)

CP = Rs. 50, SP = Rs. 66

Gain = x 100 = 32%

**Other Quants Notes:**