Important Question and solution: Maths

Important Question and solution:

11)      In a crowd of cows and hen, total head count is 22 and leg count is 60. Then how many cows n hen are ?

Solution: if 22 cows then leg count 22*4=88

So difference= 88-60=28

Then count of hen= 28/2=14 and cows=22-14=8

22)      A box contains 104 rs, which consist 25 p, 50 p & 1 rs in a ratio 1:4:2, then how many 25 p are there in the box.

Solution: 1:4:2= 4:14:8 … here 4+14+8=26

From above, 26rs consist number of coins of 25 p= 4

Then 112 rs consists= 4/26*104=16

33)      Present ratio of age of Trisha & Disha are 9:11, after 10 yrs it will become 7:8. What is the current age of both.

Solution:   

(77-72) X=(8*10-7*10)

       So, X=2

Then current age of Trisha = 9*2=18 and Disha = 11*2=22

44)      If rice of Type A cost as 60 rs/kg is mixed up with Type B cost as 70 rs/kg in such a way mixture cost becomes 64 rs/kg. Then tell the ratio of A and B in that mixture.

Solution:

Ratio of A & B= 6/4 = 3/2  …………………….this is allegation method

55)      In class V total 30 students and having avg weight of 40 kg while in class VIII, 20 students are having avg weight of 50 kg. what is the avg weight if we joint both the class?

Solution:

Here 0.2 is multiflying factor obtained from diff of weight (50-40)=10 divided by sum of students (30+20)=50… so it is 10/50=0.2

By this factor(0.2) we can get the value of a and b ,

So avg weight of joint class is 40+b or 50-a = 44 kg…………………….this is allegation method

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Input-Output:reasoning chapter 1

Input-Output:
Consider the following problem
Input  :   Sale   data  18  23  for  95  then  38
Step I :  data  sale  18  23  for  95  then  38
Step II :  data  95  sale  18  23  for  then  38
Step III :  data  95  for  sale  18  23  then  38
Step IV :  data  95  for  38  sale  18  23  then
Step V :  data  95  for  38  sale  23  18  then
Step VI :  data  95  for  38  sale  23  then  18
And step VI is last step
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Now short approach to solve this is not to see whole pattern but directly see the last step. Generally it will arrange words according to dictionary in forward or reverse manner and digits also in ascending or descending form. It could be any pattern given by the examiner, but in almost all cases you will be able to figure out the pattern by watching the last step only
In this question we can see in last step that ENGLISH alphabets are in dictionary order starting from
A to Z and numbers are in descending order, so our half work is done… as we know the pattern of the arrangement i.e. first an english letter with higher order, then highest number, then english letter in ascending number, then number just less than highest number and so on…….
One more step is to see that words are arranged in each step by shifting or swaping
Shifting : shifting means tat desire numberor alphabet comes to its place and all the words and letters are shifted as it is after that word
For eg
data  goat solo eat her zoo
now eat has to come before goat so we shift it as
data eat (goat solo her zoo) arranged as it is
Swapping : In this type one word is replaced by other one
For eg
Data goat solo eat her zoo
We swap it as
Data eat solo goat her zoo
(here eat and goat are interchanged)
Now as per the present scenario we mostly have shifting type of pattern and we have a short trick for it to find answers of question
If it is given in question that Second step of input is so and so find fifth step, so in these question instead of solving it completely, we can see that if given step is second step so AT LEAST two words are already arranged  so look at the given stucture that if 2 or 3 or how many words are arranged after that instead of writing it step by step put the step number on words with PENCIL which are arranged and then put the step number on next word which should come next and increase the counter of the steps i.e. step 3 in your mind, then put step number to the next word that should come in the arrangement and increase step counter.
In some cases after arranging a number or word, the next word seems already in arrangement, then we put same step number for that word also. In this case we will put the word or number but we will not increase the step counter as we do not have to shift it anywhere, it was already at its place.
For eg-
Data(1)  solo(3’) goat(2) eat(1’) her(3) zoo(3”)
Also as per first example, we will arrange by marking as well:
Input  :   Sale(4’)   data(1)  18(6’)  23(5)  for(3)  95(2)  then(6)  38(4)
If the Input is like: Sale  18 data  95  23  for  then  38
Then:   Sale(4’)  23(4”) data(1)  95(2)  then(4”’)  for(3)  18(4””)  38(4)
Here after arranging 4^th step, remaining words already formed the arrangement , so only 4 step needed to solve the question.
* Generally there is a question in which it is asked that step III or any step of the arrangement is given , then he asks any of the previous steps than step III or whichever step is given, step I or step II in this case. In these question the answer will be CANNOT BE DETERMINED.

SQUARE ROOT AND CUBE ROOT

!!! Before starting the chapter, I hope you will learn square of 1 to 25 and cube of 1 to 20 !!!

SQUARE ROOT:

First of all, we will see what comes as last digit after square of last digits of any number:

HINT 1: 1²=1, 2²=4, 3²=9, 4²=6, 5²=5, 6²=6, 7²=9, 8²=4, 9²=1

Here we can see square of any number cannot have last digit as 2,3,7,8. So, if any number consist these digits as last digit cannot be a perfect square.

Now, we have to determine square root of a number having ‘n’ digits.

:: If n is odd, then there are (n+1)/2 digits in its square root.

: : If n is even, then there are n/2 digits in its square root.

So, If n=1,2 then square root contains ‘1’ digit

If n=3,4 then square root contains ‘2’ digit

If n=5, then square root contains ‘3’ digit

For example- (1)square root of 729

It consist 3 digits so square root of 729 should have (3+1)/2=2 digits (_ _) in it.

And last digit should be 3 or 7 , as per HINT 1

Now for first digit determination, 729 is lies between 20²=400 & 30²=900, so first digit should be 2.

So, answer is 23 or 27. As 729 is close to 900 as compare to  400. Thus correct answer is “27”.

Example- (2)square root of 232324

It consist 6 digits so square root of 232324 should have 6/2=3 digits (_ _ _) in it.

And last digit should be 2 or 8 , as per HINT 1

Now for first two digits determination, 232324 is lies between 480²=230400 & 490²=240100, so first two digits should be 48.

So, answer is 482 or 488. As 232324 is close to 230400 as compare to  240100. Thus correct answer is “482”.

CUBE ROOT:

First of all, we will see what comes as last digit after square of last digits of any number:

HINT 2: 1³=1, 2³=8, 3³=7, 4³=4, 5³=5, 6³=6, 7³=3, 8³=2, 9³=9

Here we can see cube of any number can have last digit as 1-9.

Now, we have to determine cube root of a number having ‘n’ digits.

:: If n = 1,2,3 then cube root contains ‘1’ digit

:: If n = 4,5,6 then cube root contains ‘2’ digit

:: If n = 7,8,9 then cube root contains ‘3’ digit

For example- (1)cube root of 1331

It consist 4 digits so cube root of 1331 should have 2 digits (_ _) in it.

And last digit should be 1, as per HINT 2

Now for first digit determination, 1331 is lies between 10³=1000 & 20³=8000, so first digit should be 1.

Thus correct answer is “11”.

Example- (2)cube root of 1860867

It consist 7 digits so cube root of 1860867 should have 3 digits (_ _ _) in it.

And last digit should be 3, as per HINT 2

Now for first two digits determination, 186086731 is lies between 120³=1728000 & 130³=2197000, so first two digits should be 12.

Thus correct answer is “123”.

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Percentage

ð  Percentage

First of all remember these %-ratio  relation, this will help in solving ques:

100 %     = 1

  50 %     = 1/2

33.33 % = 1/3

      25 % = 1/4

      20 % = 1/5

16.66 % = 1/6

14.28 % = 1/7

12.50 % = 1/8

11.11 % = 1/9

      10 % = 1/10

Now three methods are there to solve the % problems:

1-      Increase-Decrease

2-      Successive Change

3-      Multiplying Factor

Increase-Decrease

Ø  It deals with ratio, if a objects is increasing with 25%=1/4 then it will be decrease by 20%=1/5 or if an object is decreasing with 25%=1/4 then it will be increase by 33.33%=1/3.

Ø  One more example if increasing by 75%=3/4, then decrease with 3/7.

Ø  And if decrease with 2/5, then increase with 2/7.

Ø  So, as per above examples we can see, if something is increasing with a/b, then it will bw decreasing with a/(b-a) and if decreasing with a/b then increase with a/(a+b)

This concept can solve many types of questions just like:

Ques 1- If area of a land is remains same and we are increasing the length by 25%, then how much % changes required in the width?

Ans 1- A= L x B, where A constant. So, A/L=B (means L and B are inversely proportional)

So if L increases, B decreases

Hence, if L is increased by 1/4 then B should be decreased by 1/5 .

Ques 2- If speed is decreased by 25% then how much more time needed to complete a particular distance?

Ans 2- Speed= Distance/Time, where Distance is constant.

So if Speed decreases, Time increases

Hence, if Speed is decreased by 1/4 then Time should be increased by 1/3 .

Ques 3- If rates of a commodity increased by 50% then what will be the effect on its consumption as per Indian market trend?

Ans 3- As per Indian market trend, Rates & Consumption are inversely proportional to each-other.

So if Rates increases Consumption decreases

Hence, if rate is increased by 1/2 then consumption should be decreased by 1/3 .

Successive change

Ø  Unit A----x%---Unit B----y%----Unit C

Then overall changes from A to C is S.C.= x+y+xy/100

If profit/increase/surcharge, then value is (+) positive

If loss/decrease/discount, then value is (-) negative

Ø  Rmember these combination represent x%, y%, S,C. %

+20 , +25 -> +50

+25 ,  -20 -> 0

 -25 , +20 -> -10

This concept can solve many types of questions just like:

Ques 1- If length of a rectangle is increased by 20% and width by 25%, then how much % changes occurs in area?

Ans 1- 20+25+20*25/100= 50 %

Multiplying Factor

           

Ø  A------x%-----B-------y%------C-------z%--------D

Then overall change from A to D=a*mf1*mf2*mf3= A*(1+x/100)*(1+y/100)*(1+z/100)

So mf1=1+x/100

This concept can solve many types of questions just like:

Ques 1- Current population=3 lakh,If population of a country increases by 10% every year, then what is the population after 3 years?

Ans 1- mf= 1_10/100= 1.1

So overall population= 3*1.1*1.1*1.1= 3.993 lakh

Conclusion- If a problem deals with only one time percentage change, Increase/Decrease trick is useful.

If there are two times changes in percentage, then Successive Change trick is good.

And if there are more than two times percentage changes exist, use Multiplying factor.

For more study material- visit my blog: studysyndrome.blogspot.in

And to read my poems- visit my blog : magicalemotion.blogspot.in