Is it just me, or does it seem strange that the root of beatification is "beat"?

(and, yes, I know that it is really Latin "beatus" -- but that begs a similar question of whether "beating someone" means you are blessing them. )

I think I will tell my daughter next time she gets in trouble that she is headed for a "blessed beating"!

>>><<<

 

On second thought, it's probably just as well to tell her that she is about to get "blessed," and leave it at that. If she inquires, I'll explain that it is in the Latin sense of the word.

 

@RRITESH KAKKAR

In the interests of your edification I offer the following illustration of two methods of simultaneous solution...

@RRITESH KAKKAR --- Please read!

I am taking a good deal of time and effort to assist your study of mathematics -- What I require in return is earnest effort and attention to instruction on your part!
Meaning, among other things, that you carefully read this post and make an honest effort at comprehension of the techniques demonstrated herein -- That includes asking questions and practicing the techniques until you are comfortable with them!

We will return to the problem of post #972 following your demonstration of proficiency at simultaneous solution...K?

As an example, we'll use the problem you suggested yesterday -- To wit:

4 men and 6 women can complete a work in 8 days, while 3 men and 7 women can complete it in 10 days. In how many days will 10 women complete it?

1) Make an algebraic 'statement of the case':

Eq1 ) 4M+6W=1/8 (i.e. 4 men and 6 women working for 1 day complete 1/8 of the job.)
Eq2 ) 3M+7W =1/10 (i.e. 3 men and 7 women working for 1 day complete 1/10 of the job.)

Where:
M = the fraction of the job completed by a single male worker per day.
W = the fraction of the job completed by a single female worker per day.

Clearly, to solve the problem we need only find the value of 'W'
//////////////////////////////////////////////////////////////////////////////////////////////////////////////////////

Simultaneous solution via 'Cancellation':
Note that, for a number of reasons, this is the preferred method of simultaneous solution...

1) Rewrite one of the equations such that a term in an unknown is the additive inverse of the term in the same unknown in the other equation:

Example:
Given Eq1 and Eq2:
4M+6W=1/8
3M+7W =1/10

Rewrite Eq2 thus:
(-4/3)*(3M+7W=1/10) = -4M-(28/3)W=-2/15 --- NOTE: Owing to its linearity, the solution set of the equation is not altered!

2) Add the equations:
4M+6W=1/8
-4M-(28/3)W=-2/15

Resultant equation: 0M-(10/3)W=-1/120

3) Solve the resultant equation for the unknown:

-10/3W=-120 → w=1/400

Thus one woman completes 1/400 of the task per day hence the task completion time for ten women = 40 days...

/////////////////////////////////////////////////////////////////////////////////////////////////////////

Simultaneous solution via 'substitution':

1) Solve either equation for either of the unknowns:

Example:
Given eq1): 4M+6W=1/8
Solve for 'M'
M=(-48W+1)/32

3) Substitute the solution in the other equation

Given eq2): 3M+7W=1/10
Substitute 'M' in with "((-48W+1)/32)

Resulting equation: 3*((-48W+1)/32)+7W=1/10

4) Solve the resulting equation for the unknown:

3*((-48W+1)/32)+7W=1/10→W=1/400

Again the solution --- One woman completes 1/400 of the task per day hence task completion time for ten women = 40 days...

Note that the techniques illustrated above may be applied to any number of linear equations containing any number of unknowns --- and, with certain qualifications, to non-linear equations...

I expect you to have questions! -- Please ask them!!!!

Best regards
HP

PS --- Note that the productivity ratio of the men to the women is 11:1 --- Aye, aye! aye! --- More slackers for @Aleph(0) to dismiss!

 

To reinforce what HP went through above, but to add the notion of units to it, let's look at the simultaneous approach again.

First, define your variables clearly:

M = The fraction of a job that one man can accomplish per day (in "jobs per day per man" or "jobs/(man·day)"
W = The fraction of a job that one woman can accomplish per day (in "jobs per day per woman" or "jobs/(woman·day)"

T = Time spent working (in "days")

J = Number of jobs completed in time T (in "jobs")

In general

J = [(#_men)·M + (#_women)·W]·T

Now convert the information in the problem to mathematical statements:

"4 men and 6 women can complete a work in 8 days"

1 job = [(4 men)·M + (6 women)·W](8 days) = (32 man·days)·M + (48 woman·days)·W

"3 men and 7 women can complete it in 10 days"

1 job = [(3 men)·M + (7 women)·W](10 days) = (30 man·days)·M + (70 woman·days)·W

Now set up an equation for what you want to solve for:

"In how many days will 10 women complete it?"

We want to know what T is if J = 1 job, M = 0 men, and W = 10 women:

1 job = (10 women)·W·T

T = (1 job)/(W·(10 women/job))

So we need to find W and we have two equations with both M and W, so we use them to eliminate M:

1 job = (32 man·days)·M + (48 woman·days)·W
1 job = (30 man·days)·M + (70 woman·days)·W

These are both equations, so as long as we do the same thing to both sides of one of them, it remains an equation. So let's multiply both sides of the top equation by 30 and both sides of the bottom equation by 32:

30(1 job) = 30[(32 man·days)·M + (48 woman·days)·W]
32(1 job) = 32[(30 man·days)·M + (70 woman·days)·W]

30 jobs = (960 man·days)·M + (1440 woman·days)·W
32 jobs = (960 man·days)·M + (2240 woman·days)·W

Remember that we can subtract the same thing from both sides of an equation and retain the equality, so let's subtract X from both sides of the bottom equation:

32 jobs - X = (960 man·days)·M + (2240 woman·days)·W - X

On the left side, we'll set X = 30 jobs, but on the right we will set X = [(960 man·days)·M + (1440 woman·days)·W]. We can do this because we have an equation telling us that these two expression are equal.

32 jobs - 30 jobs = (960 man·days)·M + (2240 woman·days)·W - [(960 man·days)·M + (1440 woman·days)·W]

2 jobs = (2240 woman·days - 1440 woman·days)·W = (800 woman·days)·W

W = (1/400) jobs/(woman·day)

Plugging this back into our goal equation:

T = (1 job)/(W·(10 women/job)) = (1 job) / {[(1/400) jobs/(woman·day)](10 women/job)} = 40 days/job

That last equation isn't very obvious when written as pure text.

 

One thousand and twenty-four posts! Is the aptitude test finding the aptitude of AAC or RRITESH?
Maybe I ask too much to think that one finds ones aptitude by taking the test using one's own abilities.
Having not read 999 of the posts, this has probably been resolved while I wasn't looking.
This post is probably moot...for several reasons.

 

One thousand and twenty-four posts! Is the aptitude test finding the aptitude of AAC or RRITESH?
Maybe I ask too much to think that one finds ones aptitude by taking the test using one's own abilities.
Having not read 999 of the posts, this has probably been resolved while I wasn't looking.
This post is probably moot...for several reasons.

My over/under was 500. That's why I don't bet on football.
But progress is being made.

 

One thousand and twenty-four posts! Is the aptitude test finding the aptitude of AAC or RRITESH?
Maybe I ask too much to think that one finds ones aptitude by taking the test using one's own abilities.
Having not read 999 of the posts, this has probably been resolved while I wasn't looking.
This post is probably moot...for several reasons.

Actually 'Aptitude Test' is merely the title of the study material chosen from the web --- it's all about drill with data sufficiency exercises --- No 'Google Glass Net' here!

Best regards
HP

 

But is not taking practice tests and learning how to understand and answer such problems one legitimate way to improve one's aptitude?

 

@RRITESH KAKKAR

Please see posts #1023 and #1024 --- Thanks!

 

(-4/3)*(3M+7W=1/10)

Understand this part was to be known.

 

(-4/3)*(3M+7W=1/10)

Understand this part was to be known.

Huh?

All he is doing is multiplying both sides of the equation by -4/3. The purpose is to change the coefficient of M to -4 so that the two equations can be added and the two terms involving M will cancel out (since one has a coefficient of -4 and the other a coefficient of +4).

 

(-4/3)*(3M+7W=1/10)

Understand this part was to be known.

The idea is to multiply the equation by a value that results cancellation of one term upon addition of the equations

 

All he is doing is multiplying both sides of the equation by -4/3. The purpose is to change the coefficient of M to -4 so that the two equations can be added and the two terms involving M will cancel out (since one has a coefficient of -4 and the other a coefficient of +4).

Yes i forgot that part.

 

@RRITESH KAKKAR

My advice is that you study post #1023 to glean the basic principles of simultaneous solution -- then study post #1024 to combine said skills with effective 'unit management'

 

@RRITESH KAKKAR

Do you wish to study math today? -- If not I've other things to do...

 

delete

 

today, some one told to study communication skill on forum.
I am searching how it work and benefits of it.
How to write in Hindi.

For now I advise sticking to one subject at a time - you're making progress at math -- no need to lose your stride!

 

For now I advise sticking to one subject at a time - you're making progress at math -- no need to lose your stride!

yes i will do it back.

Stride definition, to walk with long steps, as with vigor, haste, impatience, or arrogance

 

yes i will do it back.

I'm uncertain as to your meaning?

 

today, some one told to study communication skill on forum.
I am searching how it work and benefits of it.
How to write in Hindi.

The answer to how to write in Hindi on this forum is -- you don't!

This is an English-language only forum.