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# 5 Important Profit and Loss tricks: Part III

### Trick 1

A person loses 'A%' when he sells an item for 'X 'Rs. if he wants to make a profit of 'B%', then Example
A person loses 20% when he sells an item for 300 Rs. If he wants to make a profit of 40%, then what is the S.P.?
Solution:  S.P. = 525 Rs.

### Trick 2.

If on selling an item for 'A' Rs. a person gets profit equal to the loss if he sells it for 'B' Rs. Then if that person wants to make 'X%' profit on that item, then he should sell the item at Example
Manish sells an item for 1132 Rs. and gets profit equal to the loss if he sells it for 1564 Rs. If he wants to make 25% profit on that item then what is S.P.?
Solution:  S.P. = 1685 Rs.

### Trick 3.

If P sells an item on 'A%' profit to Q, Q sells the item on 'B%' loss to R, R sells the item on 'C%' profit to S for 'X' money. Then selling price of item by P will be Note: If the result comes +, then there is profit. If the result comes -, then there is loss.
Example
Sangeeta sold a machine at 20% profit to Sheena, Sheena sold that machine at 15% loss to Shweta, Shweta sold it at 12% profit to Suman for 3570 Rs. What is S.P. of the machine in which Sangeeta sold?  S.P. = 3125 Rs.

### Trick 4

If a corrupted shopkeeper makes x% while purchasing an item and y% while selling an item, then his profit % will be Example
A Shopkeeper cheats at 10% while purchasing an item and 10% while selling an item, by using false weight what is his gain?
Solution Profit % = 10+10+1
Profit % = 21%

### Trick 5.

After purchasing 'X' items a shopkeeper gives 'Y' items free then Discount %: Example
A shopkeeper gives 2 toys free after purchasing 8 toys. Find discount %.
Solution:  Discount % = 20%

## Some more important examples

### Example 1

Aashu sold a book at 5% loss and a Pencil at 15% profit. In the whole business he earned Rs.7. If he had sold a book at 5% profit and a pencil at 10% profit then he has earned Rs.6 more. What is the cost price of a book and a pencil?

Solution:
C.P. of book= x, C.P. of pencil= y
y×15% - x×5% = 7 ......(1)
y×10% + x×5% = 6+7 ......(2)
(1) + (2)
y×25% = 20 Rs.
y = 80 Rs.
Putting y=80 in equ. (1)
80×15% - x×5% = 7
x = 100 Rs.

### Example 2

A person bought 30 rings for Rs. 25 each. He sold 20 of them at a loss of 5%. He wants to gain 10% on the whole. Then his gain percentage on the remaining rings should be?
Solution:
C.P. of 30 rings = 30×25 = 750 Rs.
S.P. of 30 ring = 750×110% = 825 Rs.
S.P. of 20 rings = 20×25×95% =475 Rs.
S.P. of 10 remaining ring = (825-475) =350 Rs.
C.P. of 10 rings = 10×25 = 250 Rs. = 40%

### Example 3

A shopkeeper sold a box at a profit of 30% if he purchases it by 20% less and sold it at 40% profit so he earns 144 Rs. less. What is the C.P. of that box?
Solution:
Let C.P. = 100, S.P. = 130
Now, C.P. = 80, S.P. = 80×140%= 112
Now he earn 144 Rs. less
130-112 = 18 Rs.
If he earns 18 Rs less, than C.P. = 100
If he earns 144 Rs. Less, than C.P. = 100/18×144
C.P. = 800 Rs.

### Example 4

Reet purchased x mangoes at 9 rupees per mango and the same no. at 7 rupees per mango. She mixed them together and sells them at 10 rupees per mango. What is the gain or loss %?
Solution:
Average price of 2 mangoes = (9+7)/2 = 8 Rs.
C.P. = 8 Rs., S.P. = 10 Rs.
Profit= 2 Rs.
Profit % = 2/8×100 =25%

### Example 5

(i). Due to reduction of 20% in the price of rice, a man is able to buy 5 kg. more for Rs. 500. Find the original and reduced rate of sugar.
Solution: =400 Rs.
Now we can buy same quantity of rice in 400 Rs. It means we can now buy 5 kg. Rice in (500-400) = 100 Rs.
Reduced price = 100/5 =20 Rs.
Because the reduced price is 80%, then
Original price = 20/80×100 = 25 Rs.

(ii). Due to increase of 25% in the price of sugar, a man is able to buy 10 kg. less for Rs. 400. Find the original and reduced rate of sugar.
Solution: = 500 Rs.
Now we can buy same quantity of rice in 500 Rs. It means we could buy 10 kg. Rice in (500-400) = 100 Rs.
Increased price = 100/10 =10 Rs.
Because the increased price is 125%, then
Original price = 10/125×100 = 8 Rs.

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