**Quantitative Aptitude shortcut methods**

- 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.

- 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.

- 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%.

- 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/-.

- 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 1^{st} person = CP of 2^{nd} person = 1.25 X 120 = 150.

SP of 2^{nd} person = 180.

Profit % = SP/CP = 180/150 = 1.2 => 20%.

- 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.

- 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

ð SP > CP => (SP/CP) X (SP/CP) = (10/8) X (10/8) = 100/64 = 1.5625 => 56.25 % gain.

- 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

ð 1.5CP = 0.75MP (since 50% gain and 25% discount) => MP = 2CP.

- 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.

- 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)

ð CP = Rs. 16.

- 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%.

- 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%.

very useful to me