maths short trick
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mathsTRANSCRIPT
Chapter 1: PercentageDEFINITION : a percentage is a number or ratio expressed as a fraction of 100.
if we have to convert percentage into fraction than it is divide by 100.Example 1 :- if we write 45% then its equal to 45/100 or in fraction 9/20 or in decimal 0.45
if we have to convert fraction into percentage we have to multiple with 100.Example 2 :- if we write 3/5 in fraction it is equal to 60% 3/5x100=60.READ AND LEARN FOLLOWING TABLE as also known as conversion table of percentage. Learn this table it help you a lot to solve many problem.
the following fraction in red colour are MOST IMPORTANT.
Fraction Percentage1/1 100%1/2 50%1/3 33.33%1/4 25%1/5 20%1/6 16.66%1/7 14.28%1/8 12.5%1/9 11.11%1/10 10%1/15 6.66%1/20 5%1/25 4%1/30 3.33%1/40 2.5%1/50 2%1/60 1.66%1/75 1.33%1/80 1.25%1/90 1.11%1/100 1%
by this conversion table we can change fraction into percentage and percentage into fractionEX:- if we have to find 2/5 in %?In the table we know that 1/5=20%then, if we multiply both by 2then we have 1/5x2 = 2x20%answer is 2/5 = 40%so, you only to know basic fraction and percentage that given above.
in the inverse Ex. If we have to find out 1/15 fraction in percentage%?
In the table we have 1/5 = 20%then both side multiple by 1/3we get 1/15 = 6.66%
SOME BASIC QUESTION THAT IS ALWAYS ASKED IN THE EXAMSTYPE 1. if there is increase of X% and subsequently X% decrease then there is always loss / decrease in the condition.
ex. If rohan salary is increase by 50% and subsequently decrease by 50%. How much percentage loss? By trick ---- 50x50/100= 25% decrease/loss
TYPE 2.if A is P% more than B. then B is less than by A with P/(100+P)x100
ex. If radha earning is 25% more than sita. Then sita earning is how many percentage less then by radha?ans. By trick ---- 25/(100+25)x100=20% TYPE 3.If A is P% less than B. then B is more than by A formula: P/(100-P)x100
ex. If golu age is 20% less than gita than gita age is how many percentage more than golu? By trick ---- 20/(100-20)x100=25%
TYPE 4.if there is p% increase in price . how much % decrease his consumption so that his expenditure on it does not change. Formula: P/(100+P)x100
ex. If petrol price increase by 25%. How much percentage a person reduced his consumption so that his expenditure on it does not increase? ans. 25/(100+25)x100=20%
TYPE 5. if there is p% decrease in price . how much % increase his consumption so that his expenditure on it does not change. Formula: P/(100-P)x100
ex. If there is 30% decrease in eggs price. How much a person increased his consumption so that his expenditure on it does not increase? ans. 30/(100-30)x100=42.85
TYPE 6.Ex. If suman need 36% minimum mark to passed a exam but she score 24% mark and fail by 9 marks. What is the total mark?ans. Difference in % = difference in mark In that 36%-24%=12%that is 12%=9marksso, total mark = 9/12x100= 75
Profit And Loss
Type 1:- The ratio of the cost price and the selling price is 4:5. The profit percent is?a. 10 b. 20 c. 25 d. 30Ans:- 25
profit is always calculated on cost priceso, c.p=4 , s.p=5
Profit=s.p-c.p, 5-4=1 profit %= profit/cost price * 100, then, 1/4*100= 25
Type 2:- If on selling 12 notebooks a seller makes a profit equal to selling price of 4 notebook, what is his profits percentage?
a. 16.2/3b. 25 c. 50 d. None of theseAns:-50
if there is profit on selling item = selling price of an article To find profit %, simply minus 12 from 4= 8 Profit % = 4/8*100=50
Type 3:- A vender loses the selling price of 4 oranges on selling 36 oranges his loss percentage is?a. 10 b. 11.1/9 c. 12.1/2 d. None of theseAns:-10
if there is loss on selling item = selling price of an article to find loss%, simply add 36 to 4 = 40
Loss % = 4/40*100 = 10
Type 4:- Some article were brought of 6 for rs. 5. And sold at 5 for rs. 6. Gain percentage is/a. 30 b. 33.1/3 c. 35 d. 44Ans:-44
Type 5:- A vender by selling 12 toffee for a rupee. A man loses 20%. How many for a rupee should he sell to get a gain of 20%?
a. 10b. 20 c. 8 d. 12Ans:- 8
12 toffee for rs 1 loss 20% then c.p = 1*100/80 = 5/4 on this price we have to gain profit of 20% So, 5/4* 120/100 = 3/2
If for Rs. 2/3 we have 12 toffee then for rs 1 we have = 12x2/3=8
Type 6:- A sell a bicycle of to B at a profit of 20%. B sell it to C at profit of 25%. If C pays rs. 225 for it the cost price of bicycle is?
a. 110 b. 120 c. 125 d. 150Ans:- 150
let cost price be X then, x.120/100 . 125/100= 225 , by solving, then X equal to 150
Type 7:- A shopkeeper professes to sell his goods at cost price but uses a weight of 800gm instead of 1kg. thus he makes a profit of?
a. 20% b. 16.2/3 c. 25 d. 50Ans :- 25
Type 8 :- A shopkeeper cheats to the extents of 10% while buying as well as selling by using false weight his total gain is ?
a. 10% b. 11% c. 20% d. 21%Ans :-21%
Type 9 :- An article when sold at a gain of 5% yields rs. 15 more than when sold at a loss of 5%. Its cost price would be
a. 150 b. 200 c. 250 d.300Ans:-150difference between gain % and loss% equal to 10%
then, 10% = rs. 15 100% = rs. 150 , that is your cost price
Type 10:- The price of an article has been reduced by 25%. In order to restore the original price the reduced price must be increased by?
a. 25% b. 30% c. 33% d. 33.1/3%Ans:-33.1/3%
Type 11:- An article was sold at 16% gain. Had it been sold for rs. 200 more, the gain would have been 20% then the cost price of the article is?
a. 5000 b. 4800 c. 4500 d.5200Ans :- 5000
difference in gain % equal to 200, Then 20%-16%=4%
4%= 200 then, 100%= 5000 that is your cost price of the article
Work and Time
Square Roots
FIRST CASE:- NUMBER WITH LAST DIGIT 5
SECOND CASE:- SQUARE BETWEEN 30 TO 50
THIRD CASE:- SQUARE BETWEEN 50 TO 80
FOURTH CASE:- SQUARE BETWEEN 80 TO 100
FIFTH CASE:- SQUARE BETWEEN 100 TO 130
MOCK TESTQ1. Find the square of 95?a. 9125 b. 9025 c. 9225 d. 9175
Q2. Find the square of 42?a. 1763 b. 1764 c. 1765 d. 1766
Q3. Find the square of 79?a. 6233 b. 6255 c. 6241 d. 6251
Q4. Find the square of 121?a. 15252 b. 12625 c. 14625 d. 14641
Q5. find the square of 98?a. 9604 b. 9609 c. 9603 d. 9600
Cube Roots
SIMPLE INTEREST
We have using these BASIC formulas S.I. = PxRxT / 100
BUT there are some example how these shortcut tricks that
Type 1.In how many years will a sum of money double itself at 12% per annum?a. 6years 6 months b. 7 years 6 months c. 8 years 3 months d. 8 years 4 months
Type 2. at what rate of percent of simple interest will a sum of money double itself in 12 years?a. 8% b. 8.1/3% c. 8.1/2% d. 9.1/2%
Type 3.The rate at which a sum become four times of itself in 15 years at simple interest will be?a.15% b. 17.1/2% c. 20% d. 25%
Type 4.if a sum of money at simple interest double in 6 years. it will become 4 time in ?a. 12 years b. 14 years c. 16 years d. 18 years
Type 5.How long will it take a sum of money invested at 5% p.a. by simple interest to increase it value by 40%?a. 5 years b. 6 years. c. 7 years d. 8 years
COMPOUND INTEREST SHORTCUT TRICKS
Type 1.a sum of money place at compound interest double itself in 5 years. It will become 8 times itself at same rate of interest in ?a. 7 years b. 10 years c. 15 years d. 20 years
Type2.By C.I. at 10 % p.a. a sum increased to 2662 in 3 years what will be the principal amount ?a. 1000 b. 1500 c. 2000 d. 2500
Type 3.
In C.I, what will be the rate of interest if a sum becomes 1331 in 3 years?a. 100b.1000c.10000d. none of these