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

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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:
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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
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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:
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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
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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?
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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
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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
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Profit % = 10+10+1
Profit % = 21%

Trick 5. 

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