Mathematics/Numerical ability shortcuts for all competitive exams

Okay, I would post a brief explanation of how to take L.C.M .

 

L.C.M As one of our Ilites have asked how to take L.C.M:-

I am explaining in detailed steps and methods: ( I hope this would help for people who are confused or have doubts on L.C.M subject)

Method 1:


1) Find L.C.M of 2/3 + 5/4

So in numerators we have 2, and 5 and in Denominators we have 3 and 4.

Step1:- we have to find L.C.M for denominators numbers

Now we have to find common multiples for both denominators.

3 * 4 = 12

2/3 + 5/4 = (4 * 2 + 5 *3)/12

====> ( 8 +15)/12 == 23/12

The answer is 23/12

All you have to find is least common multiples from the given denominators.

Problem 2:


1/3 + 2/6 + 5/18

Explanation:

From the given sum, we have to find least common multiples, so we could take 18 as L.C.M because denominators, 3, 6, can be multiplied by 18

3 * 6 = 18 ==> ( 1 * 6 =6)
6* 3 = 18 ===> ( 2* 3 = 6)
1* 18 = 18 ====>( 5 * 1 = 5)

Now the answer is ( 6+6 +5)/18 ==> 17/18


Problem 3:

4/5 + 7/60

Explanation:

From the given sum, we have to find least common multiples for both denominators.

So , the denominators are 5 and 60, and 60 is a multiple of 5, so we could assume 60 as L.C.M

4/5 + 7/60 = ( 4* 12+ 1* 7) /60

Here, 4 * 12 denotes Numerator * ( L.C.M/Denominator).

Hope this clears your L.C.M basic explanation. If you need more sums on various problems, I would explain and provide you exercises.:thumbsup

1) How to find L.C.M for ( 2/5 + 1/3+ 3/ 4)

So in denominators we have 5, 3, 4 and we have to find common multiples for them.

i.e 5 * 4* 3 = 60

the L.C.M of this given problem is 60.

60/5 = 12==> 12 * 2 = 24/60
60/3= 20==> 20* 1= 20/60
60/4= 15 ==> 15*3 =45/60

Now sum it up ====> 89/60

 

Please find my previous lessons I have mentioned how to find square of a number and square root.

 

Pipes and Cisterns problems are like Time and Work the only difference is days and hours in Time and work

Hours and minutes in Pipes and Cisterns.

Yes, I would explain abt it.

 

For Pipes and Cisterns Sum, they would ask the question like this:

Eg:-1

Two pipes A and B can fill or empty a cistern in X and Y hours respectively while they working alone. If both the pipes are opened together, then time taken to fill or empty the cistern is given by


XY
----
X+Y


Now lets see a problem :

Two pipes A and B can fill a Cistern 20 and 30 minutes respectively. If both the pipes are opened simulatenously, how long will it take to fill the cistern?



Solution:


Here X = 20, y = 30 minutes

So apply the formula:

1/x + 1/y ==> 1/20 + 1/30 ===> 5/60 ( Note, I have taken L.c.M, I hope most of you know how to do this L.C.M step)

Simplyfying 5/60====> 1/12

So, The answer is Both the pipes A and B fill the cistern together in 12 minutes.