When the price of the radio was reduced by 20% its sales is increased by 80% What was the net effect on the sale?

Railway Recruitment Board Computer Based Test>Percentage>Exercise 6>Q 21

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Percentage

1. Change a percentage into fraction:
a%=a100 2. Change a fraction into percentage:

xy=xy×100%

3. y% of x=x×y100
4.If the price of a commodity increases by x%, then the reduction in consumption so that the expenditure remains constant can be found using this formula:
x100±x×100% 5. Here, the positive sign represents an increase in price and the negative sign represents a decrease in price.

6. If x is a% more than y, then y is less than x by a100+a×100%

7. If x is a% less than y, then y is more than x by a100−a×100% 8. Successive increase:

9. If a value is increased by x% and then by y%, then the successive increase will be given by:

x+y+xy100%

10. Successive decrease:
11. If a value is decreased by x% and then by y%, then the successive decrease will be given by:
x+y−xy100%

Profit and Loss
1. Gain = Selling Price – Cost Price
2. Loss = Cost Price – Selling Price 3. Loss or gain is always reckoned on the cost price.

4. Gain percentage = Gain Cost Price ×100

5. Loss percentage = Loss Cost Price ×100
6. Selling Price =100+Gain%100× Cost Price
7. Selling Price =(100−Loss %)100× Cost Price
8. Cost Price =100(100+Gain %)× Selling Price
9. Cost Price =100(100−Loss%)× Selling Price
10. If an article is sold at a gain of x%, then Selling Price =(100+x)% of Cost Price
11. If an article is sold at a loss of x%, then Selling Price =100–x% of Cost Price
12. When a person sells two similar items, one at a gain of p% and other at a loss of p%, then the seller always incurs a loss.
Loss Percentage = Loss and Gain Percent 102=p102
13. If a shopkeeper or trader professes to sell his goods at cost price, but he uses false weights, then, Gain Percentage =ErrorTrue Value-Error×100%=True weight-False weightFalse weight×100%
14. If a shopkeeper or trader sells his goods at x% loss on cost price but uses y gram instead of z gram, then profit or loss percentage will be given by (100−x)zy−100%. [Positive result indicates profit and negative result indicates loss.]
15. If a shopkeeper or trader sells his goods at x% profit or loss on the cost price and uses y% less weight, then his profit or loss percentage will be given by (y±x)100−y×100%. [Positive result indicates profit and negative result indicates loss.]
16. If xth part of some items is sold at p% loss, then the required gain percent in selling the rest of the items in order that there is neither gain nor loss in the whole transaction, is xp1−x%.
17. A trader sells his items at a gain/loss of x%. If he had sold it for ₹P more, he would have gained/lost y%. Then, Cost Price of item =Py±x×100.
(‘-’ when both are either profit or loss, ‘+’ when one is profit and other is loss.)
18. If the cost price of x articles is equal to the selling price of y articles, then profit percentage =x−yy×100%.
19. If a person purchases a items for ₹P and sells b items for ₹Q, then the profit or loss percent is given by aQ−bPbP×100%. [Positive result means profit and negative result means loss.]

20. If X sold an article to Y at a profit or loss of a1% and Y sold the same article to Z at a profit or loss of a2%, then the cost price of the same article for Z is given by

Cost Price for X×1±a11001±a2100. [Positive sign will indicate profit and Negative sign will indicate loss.]

21. If x part of an article is sold at p% profit or loss, y part at q% profit or loss and z part at r% profit or loss and finally, there is a profit or loss of ₹R, then Cost Price =R×100xp+yq+zr.

[If p, q and r is positive, it indicates profit, and if p, q and r is negative it indicates loss.]
22. If there are two successive profits or losses at x% and y%, respectively, then resultant profit or loss is given by x+y+xy100%.
[If x or y is positive, it indicates profit, and if x or y is negative it indicates loss.]
23. Discount = Marked Price – Selling Price
24. Discount %=DiscountMarked Price×100=Marked Price-Selling Price Marked Price×100
25. Selling Price = Marked Price ×1−x100, where x% is the rate of discount allowed.
26. Selling Price = Marked Price – Discount 27. Discount is always calculated with respect to the marked price of an article.

28. Single discount equivalent to two successive discounts x1% and x2%=x1+x2−x1×x2100%.

29. Single discount equivalent to three successive discounts x1%,x2% and x3%=1−1−x11001−x21001−x3100×100%.
30. If a shopkeeper or trader wants a profit of x% after allowing a discount of y%, then
Marked Price of the item =CP100+x100−y.
31. If a shopkeeper or trader wants a profit of x% after allowing a discount of y%, then
Cost Price of the item =MP100−y100+x.
32. A shopkeeper or trader fixes the marked price of an article in such a way that after allowing a discount of x%, he earns a profit of y%, then Marked Price of the article is x+y100−x×100% more than its Cost Price.
33. If a shopkeeper or trader allows a discount of x1% on an article and the marked price of the article is y% more than the cost price, then
Profit or loss percent in the whole transaction is y×100−x1100−x1
[Positive result will indicate profit and negative result will indicate loss.]

Simple and Compound interest

1. Amount = Principal + Interest
2. Simple interest (SI)=P×R×T100
Where P is Principal, R is Rate and T is Time.
3. Compound interest (Cl)=P1+R100T−P
Where P is Principal, R is Rate and T is Time. 4. Compound interest, if compounded half-yearly

Compound interest (Cl)=P1+R2002T−P

5. Compound interest, if compounded quarterly

Compound interest (Cl)=P1+R4004T−P

6. Compound interest, if compounded monthly

Compound interest (Cl)=P1+R120012T−P

7. Interest is compounded annually but time is in fraction, say 347 years
Compound interest (Cl)=P1+R10031+4R7×100−P
8. Compound interest when rates are different for each year =P1+r11001+r2100…−P
9. The difference between simple and compound interest for 2 years
Difference = Principal×r1002
The difference between simple and compound interest for 3 years
Difference = Principal ×r2(300+r)1003
10. Population after n years
Population after n years while the rate is the same for each year =P1±r100n
Population after n years while the rate is different for each year =P1±r11001±r2100… Here, the positive sign represents increase in population and the negative sign represents decrease in population.

11. Population n years ago

Population n years ago =P1±R100n Here, the positive sign represents increase in population and the negative sign represents decrease in population.

12. Value of Machine after n years =P1±r100n

Here, the positive sign represents increase in price and the negative sign represents decrease in price.

13. Value of Machine n years ago =P1±R100n

Here, the positive sign represents increase in price and the negative sign represents decrease in price.

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