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# Profit & Loss

1.

If Arko sells an article at $$\frac{4}{5}$$th of its selling price and secures a profit of $$20$$%, what will be the profit or loss percentage if he sells it at the actual selling price?

Let Cost Price is $$Rs. 100$$

Profit $$20$$% Means $$\Rightarrow 120.$$

$$120 = \frac{4}{5SP} \Rightarrow SP = 150.$$

Then profit percentage is $$50$$%

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2.

A person $$X$$ sold an Item to $$Y$$ at $$40$$% loss, then $$Y$$ sold it to third person $$Z$$ at $$40$$% profit and finally $$Z$$ sold it back to $$X$$ at $$40$$% profit. In this whole process what is the percentage loss or profit of X?

Let the Cost Price $$= Rs. 100.$$ for $$X.$$

$$Y's$$ Cost Price $$= Rs. 60.$$

$$Z's$$ Cost Price $$= Rs. 84.$$

Finally, $$X's$$ Cost Price $$RS. 117.6.$$

$$\therefore X's$$ loss $$117.6 - 60 = Rs. 57.6$$

$$\therefore X's$$ loss percentage $$= 57.6$$%

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3.

In a certain store, the profit is 270% of the cost. If the cost increases by 30% but the selling price remains constant, approximately what %ge of the selling price is the profit.

Let Cost Price $$= Rs . 100.$$

Then, Profit $$= Rs. 270,$$

Selling Price $$Rs. 370.$$

New Cost Price $$= 130$$% of $$Rs. 100 = Rs. 130$$

New Selling Price $$= Rs. 370.$$

Profit $$= Rs. (370 - 130) = Rs. 240$$

Required  percentage $$= (\frac{240}{370}) \times 100 = 64.86 = 65$$% (approx)

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4.

The percentage profit earned by selling an article for $$Rs. 2120$$ is equal to the percentage loss incurred by selling the same article for $$Rs. 1520.$$ At what price should the article be sold to make $$25$$% profit?

The Cost Price be

$$2120 + 1500 = 3640$$

$$\frac{3640}{2} = 1820.$$

Selling Price $$= \frac{1820 \times 125}{100} = \frac{1820 \times 5}{4}$$

$$= Rs 2275$$

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5.

Profit earned by an organisation is distributed among officers and clerks in the ratio of 5 : 3. If the number of officers is 55 and the number of clerks is 70 and the amount received by each officer is Rs12,000, what was the total amount of profit earned?

The total amount distributed among 55 officers $$= Rs. 55 \times 1200 = Rs. 6,60,000.$$

Their ratio $$5:3$$

Total profit $$= 6,60,000 + 396000 = Rs 10,56,000.$$