Profit and Loss

Profit and Loss

Profit and Loss

The term Profit and Loss is used in business. In business transaction goods are purchased and sold. The price used to purchase is called “Cost Price” and written as CP. The price obtained by selling goods is called “Selling Price” and it is written as SP. If selling price of certain goods is more than the cost price, then there is a profit. If cost price of certain goods is more than its selling price, then there is a loss. For example:

-    An article is bought for Rs. 500 and sold it for Rs. 600. Here, SP is more than CP, so there is a profit of Rs. 600 – 500 = Rs. 100.

-    An article is bought for Rs. 1000 and sold for Rs. 800. Here, CP is more than SP, so there is a loss of Rs. 1000 – 800 = Rs. 200

As stated in the above examples:

If SP>CP, there is a profit and it is obtained as

Profit (P) = SP – CP

If CP>SP, there is loss and it is obtained as

Loss (L) = CP – SP

Profit and loss percent are calculated on the basis of cost price (CP). So,

Profit percent (P%) = Profit/CP × 100%.  Loss percent (L%) = Loss/CP × 100%


List of formulae on CP, SP, Profit and Loss

1. Profit = SP – CP  	2. Loss = CP – SP  	3. SP = CP + Profit 	4. CP = SP – Profit 	5. SP = CP – Loss 	6. CP = SP + Loss 	7. Profit percent (P%) = Profit/CP × 100% 	8. Loss percent (L%) = Loss/CP × 100% 	    9. CP = 100/(100 + P%) × SP 	10. CP = 100/(100 - L%) × SP 	11. SP = (100 + P%)/100 × CP 	  12. SP = (100 - L%)/100 × CP


How to solve the problems related to Profit and Loss?

While solving the problems related to profit and loss we must use the following steps:

i.     Understand the problem and make planing.

ii.    Solve problem according to the planing.

iii.  Review solved problem and recheck  it.

iv.  At last, write the conclusion according to the question.



Workout Examples

Example 1: Mrs. Sarala bought a Banarasi Sari at Rs 3500. After one month, she was interested to have a new one and hence she sold it for Rs. 3200. Find her loss percent.

Solution: Here,

CP = Rs. 3500, SP = Rs. 3200 ∴  Loss = CP – SP  	= Rs. 3500 – 3200  	= Rs. 300 ∴  Loss percent = Loss/CP × 100% 		  = 300/3500 × 100% 		  = 8.57%

  Her loss percent is 8.57%.

 

Example 2: Sabin bought 14 copies for Rs. 140 and sold 8 copies for Rs. 96. Find his profit or loss percent.

Solution: Here,

CP of 14 copies = Rs. 140 ∴  CP of 1 copy = Rs. 140/14 = Rs. 10     SP of 8 copies = Rs. 96 ∴  SP of 1 copy = Rs. 96/8 = Rs. 12 ∴  For 1 copy, SP > CP. So there is profit. ∴  Profit = SP – CP  	  = Rs. 12 – 10  	  = Rs. 2 ∴  Profit percent = Profit/CP × 100% 	                = 2/10 × 100% 		     = 20%

He has got profit of 20%.

 

Example 3: An exercise book cost Rs. 20. If it is sold at a profit of 10%, find its selling price.

Solution: Here,

CP = Rs. 20,  Profit = 10%,  SP = ? We know, 	SP = (100 + P%)/100 × CP  	     = (100 + 10)/100 × 20 	      = 110/100 × 20 	       = Rs. 22

  Selling price of that exercise book is Rs. 22.

 

Example 4: If a shopkeeper sells a shirt for Rs. 270 at a loss of 10%, for what price should it be sold, so as to get a gain of 30%?

Solution: Here,

1st Case, 	    SP = Rs. 270,  Loss = 10% 	    ∴  CP = 100/(100 - L%) × CP 		 = 100/(100 - 10) × 270 		 = 100/90 × 270 		 = Rs. 300 2nd Case, 	    CP = Rs. 300,  Profit = 30% 	    ∴  SP = (100 + P%)/100 × CP  	             = (100 + 30)/100 × 300 	             = 130/100  × 300 	             = Rs. 390

The shirt should be sold at Rs 390 to get a profit of 30%.

 

Example 5: Salman sold a DVD at a gain of 8%. Had it been sold for Rs. 75 more, the gain would have been 14%. Find the cost price of the DVD.

Solution: Here,

Let, CP = Rs. x ∴ SP1 at 8% gain = (100 + P%)/100 × CP 		     = (100 + 8)/100 × x 		     = 108x/100 ∴ SP2 at 14% gain = (100 + 14)/100 × x 		       = 114x/100 According to question, SP2 – SP1 = Rs. 75 i.e. 	114x/100 – 108x/100 = 75  or,	(114x-108x)/100 = 75 or,	6x/100 = 75 or,	6x = 7500 or,	x = 7500/6 or,	x = 1250

Hence, the CP of DVD is Rs. 1250.


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