Mathematics profit and loss

!! Profit Loss tricky solution !!
12 good questions with tricky solution

1. A trader uses a 800gm weight instead of 1 kg. Find his profit %.
Soln: (He is buying 800 gm but selling 1000 gm.
So, CP is for 800 gm and SP is for 1000 gm.)
SP/CP = 1000/800 = 1.25 => 25% profit.

2. A trader uses 1 kg weight for 800 gm and increases the price by 20%. Find his profit/loss %.
Soln: 1 kg weight for 800 gm => loss (decrease) => 800/1000 = 0.8
20% increase in price => profit (increase) => 1.2
So, net effect = (0.8) X (1.2) = 0.96 => 4% loss.

3. A milk vendor mixes water to milk such that he gains 25%. Find the percentage of water in the mixture.
Soln: To gain 25%, the volume has to be increased by 25%.
So, for 1 lt of milk, 0.25 lt of water is added => total volume = 1.25 lt
% of water = 0.25 / 1.25 X 100 = 20%.

4. A trader bought an item for Rs. 200. If he wants a profit of 22%, at what price must he sell it?
Soln: CP=200, Profit = 22%.
So, SP = 1.22CP = 1.22 X 200 = 244/-.

5. A person buys an item at Rs. 120 and sells to another at a profit of 25%. If the second person sells the item to another at Rs. 180, what is the profit % of the second person?
Soln: SP of 1st person = CP of 2nd person = 1.25 X 120 = 150.
SP of 2nd person = 180.
Profit % = SP/CP = 180/150 = 1.2 => 20%.

6. A milk vendor mixes water to 20 lt of milk such that the ratio of milk and water is 4:3. He sold the mixture at Rs. 12 per liter but bought the milk at Rs. 10 per liter. Find the profit % of the vendor.
Soln: milk : water = 4:3 => he bought 4 parts (milk) but sold 7 parts (mixture)
CP = 10 and SP = 12.
So, profit % = (SP/CP) X (SP/CP) = (7/4) X (12/10) = 2.1 => 110% gain.

7. A trader buys some apples at a price of 10 apples for Rs. 8 and sold them at a price of 8 apples for Rs. 10. Find his profit or loss %.
Soln: He bought 10 apples for Rs. 8 and sold 8 apples for Rs. 10 => clearly got profit
SP > CP => (SP/CP) X (SP/CP) = (10/8) X (10/8) = 100/64 = 1.5625 => 56.25 % gain.

8. A trader allows a discount of 25% on his articles but wants to gain 50% gain. How many times the CP should be marked on the items?
Soln: CP applied with profit = MP applied with discount = SP
1.5CP = 0.75MP (since 50% gain and 25% discount) => MP = 2CP.

9. By selling an item at a price a trader gains 40%. What is the profit / loss % if the item is sold at half the price?
Soln: SP =1.4CP => (SP/2) = 0.7CP => 30% loss.

10. A trader gets a profit of 25% on an article. If he buys the article at 10% lesser price and sells it for Rs. 2 less, he still gets 25% profit. Find the actual CP of the article.
Soln: 25% gain => SP = 1.25CP…..1.
Now, CP is 10% less => 0.9CP and SP is Rs. 2 less => (SP-2).
Still, profit is 25% => (SP-2)=1.25(0.9CP) , where SP = 1.25CP (From 1)
CP = Rs. 16.

11. A trader gets a discount of 20% from the dealer and marks it at 20% more price then the actual MP to the customer. Find his overall gain %.
Soln: Let MP be the price on the item.
Then, CP=0.8MP (20% discount) and SP = 1.2MP.
So, gain => SP/CP = 1.2/0.8 = 1.5 => 50%.

12. A trader allows a discount of 20% to the customer after marking the item up by 25%. Find his gain/loss% if he is given a commission of 20% of the MP by the dealer.
Soln: Trader’s SP = 0.8 X (1.25MP) = MP (since 20% discount on 25% raised price)
Trader’s CP = 0.8 MP (20% commission)
So, gain = SP/CP = MP/0.8MP = 1.25 => 25%.

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