### 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.?

### 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 % = 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%

Solution:

## 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:__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.

= 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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