Averages and Mixtures problems | Formulae Shortcuts questions

Mixture and Alligation Shortcut Methods

 

Formulae:

1.       Average = sum of quantities/number of quantities

2.       Sum = avg * no. of quantities

3.       If the numbers are in A.P. (Arithmetic Progression), then the avg of numbers is given by

Avg = sum/n =[ (n/2)(a+l)]/n

                = (a+l)/2

Where  n – no. of quantities

                a – first term or value

                l – last term or value

4.       Weighted Average:

Section1:

                No. of quantities: m

                Avg of section1: p

Section2:

                No. of quantities: n

                Avg of section1: q

Avg of section1 and section2 = (m*p + n*q)/(m +n)

Points to remember/Shortcuts

1.       Average lies between minimum and maximum values.

a.       Avg > minimum value

b.      Avg < maximum value

2.       If every quantity is increased/decreased by ‘k’ value, then the avg also get increased/decreased by the same ‘k’ value.

time and work questions solutions

Time and work questions solutions 

Difficulty Level - Medium

      

      1.     A can work on 1km railway track in 1 day. In how many days, will he able to complete the work on 12km railway track?

Soln: no. of days = total work / work done in 1 day

Therefore, no. of days taken = 12/1 = 12 days

      2.     A can complete the work in 15 days. What fraction of work will be completed in 1 day?

Soln.:   Let the total work is 1 unit.

Work in 1day = total work/no. of days to complete

                                    = 1/15^th of work

      3.     A can do a piece of work in 3 days and B can do a piece of work in 5 days. In how many days will the work be completed if both A and B work together?

Soln.: Using formula:

                  Work done by A in 1 day = 1/3

                  Work done by B in 1 day = 1/5

                  Total work done by A and B in 1 day = 1/3 + 1/5 = 8/15

                  Therefore, no. of days to complete work by A and B together = 1/(Total work) = 1/(8/15) = 15/8 days which is less than 3 and 5

    Using shortcut/analysis/assumption

                  Let us consider the total work be 15 units (LCM of 3 and 5)

                  So work done by A in 1 day = 15/3 = 5 units

                  Similarly work done by B in 1 day = 15/5 = 3 units

                  So total work done by A and B in 1 day = 5 + 3 = 8 units

                  Therefore, no. of days to complete total work i.e. 15 units = total work/work done in 1 day = 15/8 days

       

      Note:

                a.     Work done by A and B in 1 day will always be greater than that of A and B individually

          b. No. of days taken by A and B together will always be less than that of A and B individually

      4.     A can do a piece of work in 6 days, B can do a piece of work in 4 days and C can do a piece of work in 12 days. Find the no. of days to complete the work if A, B and C work together?

Soln.: Using formula:

                  Work done by A in 1 day = 1/6

                  Work done by B in 1 day = ¼

                  Work done by C in 1 day = 1/12

                  Total work done by A, B and C in 1 day = 1/6 + ¼ + 1/12 = 12/24 = 1/2

                  Therefore, no. of days to complete work by A, B and C together = 1/(Total work) = 1/(1/2) = 2 days which is less than 4, 6, 12

      Using shortcut/analysis/assumption

                  Let us consider the total work be 24 units (LCM of 4, 6, 12)

                  So work done by A in 1 day = 24/4 = 6 units

                  work done by B in 1 day = 24/6 = 4 units

                  work done by C in 1 day = 24/12 = 2 units

                  So total work done by A, B and C in 1 day = 6 + 4 + 2 = 12 units

                  Therefore, no. of days to complete total work i.e. 24 units = total work/work done in 1 day = 24/12 = 2 days

The above Note is valid here as well.

      5.     A can do a piece of work in 6 days and B can do a piece of work in 12. Find the no. of days to complete the work if A and B work alternatively?

Soln.: Using formula:

                  Work done by A in 1 day = 1/6

                  Work done by B in 1 day = 1/12

                  Total work done by A and B working 1 day each = 1/6 + 1/12 = 3/12 = ¼

                  Therefore, 1/4^th of work is done in 2days.

                  No. of days to complete total work if A and B work alternatively = 1/((1/4)/2) = 8 days

      Using shortcut/analysis/assumption

                  Let us consider the total work as 12 units (LCM of 6, 12)

                  So work done by A in 1 day = 12/6 = 2 units

                  work done by B in 1 day = 12/12 = 1 unit

                  Total work done by A and B working 1 day each = 2 + 1 = 3 units in 2 days

                  Therefore, work done in 1 day = work/no. of days = 3/2 units

                        No. of days to complete work = total work/work in 1 day = 12/(3/2) = 8 days

      6.     30 men can complete a job in 40 days. Then 25 men can complete the same job in how many days?

Soln.: As per M1D1 = M2D2

               30 * 40 = 25 * x  => x = 30 * 40/25 = 48 days

      7.   30 men can complete 1500 units in 24 days working 6hrs a day. In how many days can 18 men can complete 1800 units working 8 hrs a day?

Soln.: As per the formula  (from my earlier blog), M1D1h1/W1 = M2D2h2/W2

          => 30*24*6/1500 = 18*x*8/1800

          => x = 36 days

      8.     A and B can do a work in 10 and 15 days respectively. Then combinedly A & B, in how many days the work will be completed?

      Soln.: As per the formula  (from my earlier blog), x*y/(x + y)
               A and B together can complete the work in 10 * 15/(10 + 15) = 6 days

      9.   A can do a work in 10 and, A and B together can do a work in 6 days. In how many days B can complete the same work?

      Soln.: As per the formula  (from my earlier blog), x*y/(x - y)
               B alone can complete the work in 10 * 6/(10 - 6) = 15 days

      10.  A is twice faster than B and B can complete in 12 days alone. Find the number of days to complete if A and B together work?

            Soln.: Given B works in 12 days

      A is twice faster than B => A takes 2 times less time than B

      Therefore, A completes work in 12/2 = 6 days

            A and B together can complete in 12 * 6/(12 + 6) = 4 days

 

Time And Work questions formula for placement

Time And Work questions formula for placement

1.     Work from Days:

If A can do a piece of work in n days, then A's 1 day's work =	1	.
	n

2.     Days from Work:

If A's 1 day's work =	1	,	then A can finish the work in n days.
	n

3.     Ratio:

If A is thrice as good a workman as B, then:

Ratio of work done by A and B = 3 : 1.

Ratio of times taken by A and B to finish a work = 1 : 3.

4.     No. of days = total work / work done in 1 day

5.     Relationship between Men and Work

More men         ------- can do ------->             More work

Less men         ------- can do ------->             Less work

6.     Relationship between Work and Time

More work        -------- takes------>               More Time

Less work         -------- takes------>               Less Time

7.     Relationship between Men and Time

More men        ------- can do in ------->          Less Time

Less men          ------- can do in ------->          More Time

8.     If M₁ persons can do W₁ work in D₁ days and M₂ persons can do W₂ work in D₂ days, then 

        

9.     If M₁ persons can do W₁ work in D₁ days for h₁ hours and M₂ persons can do W₂ work in D₂ days for h₂ hours, then

 Note:  If works are same, then M1D1h1 = M2D2h2 

10.  If A can do a work in ‘x’ days and B can do the same work in ‘y’ days, then the number of days required to complete the work if A and B work together is

11.  If A can do a work in ‘x’ days and A + B can do the same work in ‘y’ days, then the number of days required to complete the work if B works alone is

HOW TO MAKE SEO FRIENDLY BLOGGER | SEO TIPS FOR MAKING SITE SEO FREE

BLOGGER SEO TIPS AND TRICKS  BLOGGER | BEST WAY FOR MAKING BLOGGER SEO FRIENDLY

As we know about blogger is group of google and very good for posting articles and posting knowledgeable posts.You  should know about how to use blogger or other blogger type websites for posting articles or getting high ranking in google search results.If you understand what to do for getting high ranking in google or other search engines then it will be benefit for your websites. Okay lets start about seo. 

Let's We Start Seo for Blogger

Step :- A

 Select all the key words which are useful  for your website and describes all about your page.Be careful  to select keywords, you can use google key word toll for making good key word or we can say hot key word for your page.

Step :- B

After the making list of hot key words , you need to place these hot key words in your post for this you should use key word density tool to check key word density in your post. If the key word density crosses a limit then it gives bad impact in search results.

Step :- C

In this picture some area is highlighted with red color, very important when you are going to post in blogger .

Now i am telling you about all so be careful when u read these steps

.

Step :- D

Post Title

This one is the very most important section of blogger. When you are going to search any thing then search engines firstly read the post title of the page if post title matches with the search then it shows your page at first link. So it is very important to select the post title for this purpose you can use google search results more the search number more the competition , so always try to chose post title which has law search numbers in google.

Permalink in blogger

Permalink in blogger is also very very important for best seo friendly websites. So you have to chose custom permalink in blogger. It reflects your page with your post title so this good for google search result and getting top rank in search engine as well as affects the ranking factor. 

Labels in blogger 

Labels are also most important to make seo friendly site and to get more traffic. Always try to select labels which are related to your post. If you are using labels but they are not using in your post then it gives negative feedback to google search engine.So always select labels which has low competition in google search result.   

                                                                                      After this i will tell you one more thing that is related to labels and have very big roll in making seo friendly websites and to give higher traffic.

Location in blogger 

According to new updates in google search engine algorithms, locations is to be set when you are going to post. When you set location in google blogger then it gives an opportunity to your page to be show by google in google events. When you set location in post article then it gives a positive feedback to google search results, and show your page in top result in google.

Step :- F

After the step D , you have to make some changes in your html coding, Its not a big  task you have to follow some steps and in your blogger.

blogger title optimization for seo friendly site  

Follow these steps :-

1. Blogger > Template > Edit HTML
2. Search for the below code in the <head> section of your template
   

   <title><data:blog.pageTitle/></title>

3. Replace it with the below code
   

   <b:if cond=’data:blog.pageType == &quot;item&quot;’>
   <title><data:blog.pageName/> | <data:blog.title/></title>
   <b:else/>
   <title><data:blog.pageTitle/></title>
   </b:if>

   
   
4. Now, save your template.

Note :- After making your site seo friendly these,  take back up for all html code.

Search Engine Optimization In  Your Post Title Heading 

IN google these kind of settings  are  predefined but you have to change for getting more traffic or making seo friendly blog. Blogger  use H1 for homepage title, H2 for blog description and H3 to post titles. Due to the fact that the post titles are the second most important part of your blog after the main title, you should assign them an H2 instead of H3. By changing this your post title is optimize for getting higher result .

1. Go to Template  then  Edit HTML
2. Search for (Press Ctrl + F) then search .post h3 and replace all the occurrences of it with .post h2.
3. Next search for,
   

   <h3><data:title/></h3>

4. Replace it with the below code that is bellow 
   

   <h2><data:title/></h2>

5. Save template.

Step :- G

How the Meta Description is important in blogger

As we know about meta descriptions are very important for making blogger seo free as well as seo friendly websites .For making seo friendly Blogger some html changes have been done . These changes to google to index your page as u provide the meta description. Meta descriptions tells to google what site contains . According to meta description google decides the page ranking and page category in google webmaster. For getting High ranking in google search engine meta descriptions as well as meta tags are very important. for this these changes can be done by go to edit html for this follow this

Go to Blogger Dashboard>> Settings >> Search preferences > Meta tags > Description and click the Edit link.

and the put meta description 

Step :- H

What is Robots.txt Settings for Blogger

The robots.txt file in google is predefined setting but it is not good for making blogger seo free so you need to make some changes in robot.txt file.
changes can be done by following steps but first you need to clear all about this file.

Settings > Search Preference > Enable ‘Custom robots.txt’ under ‘Crawlers and indexing’ section and use the below text.

User-agent: Mediapartners-Google
Disallow:
User-agent: *
Disallow: /search/
Disallow: /search?
Disallow: /search?q=*
Disallow: /*?updated-max=*
Disallow: /p/about.html
Disallow: /p/privacy.html
Allow: /

Sitemap: http://http://electronics4projects.blogspot.in//atom.xml?redirect=false&start-index=1&max-results=500

Step :- I

For making seo free blogger you have to Add No Follow Tag to All Labels in your blogger.

Follow these steps

<a expr:href=’data:label.url’ rel=’tag’>

<a expr:href=’data:label.url’ rel=’tag,nofollow’>

Save your template.

Custom Robots Header Tags in blogger

Custom Robots are also very important for making seo friendly blogger .By some changing in  Custom Robots you can easily get higher traffic from search engines and peoples

How Sitemap is important in  Blogger to Google & Bing

Site maps are very important for search engines because of according to site maps google search engines as well as other search engines indexed your pages in their directory list for showing results according to the search tag. site maps are very important to making a site and blogger seo free and seo friendly.
For this you have to just use google webmaste tools as well as you can use bing webmaster tool for this.

BLOGGER SEO TIPS AND TRICKS | 10 steps for making blogger seo free | how to make blogger seo friendly 

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