I never suggested this:
Current Population (given) = 1,50,000
Population 2 years back = 1,35,375 (calculated as 1,50,000 * 0.95 * 0.95)
Population 1 year back = 1,42,144 (calculated as 1,35,375 * 1.05)
Current Population = 1,49,251 (calculated as 1,42,144 * 1.05)
On the contrary, what I proposed was:
If you know the formula for the compound interest, take the present
population as the principal and solve it.
I am writing the formula for the same.
Principal * (1+ rate /100) ^N times
Putting this formula and substituting the numbers:
1,50,000 (105/100) ^2 = 165375. This is the answer of the first part.
Now the second part is: What was the population two years back.
For this:
150000 (100/105) ^ 2 =
136054.4
----- Original Message -----
From: "Zujar Shabbir Kanchwala" <zujarbri...@gmail.com>
To: <accessindia@accessindia.org.in>
Sent: Tuesday, June 25, 2013 12:10 AM
Subject: Re: [AI] help me in understanding the method for solving such
typeof mathematical problems
@Mr. Sawhney: I wrote the earlier email to provide a method of solving the
problem at hand, not to spoon feed with exact numbers. If I write 15000
instead of 150000, it should not be so difficult to find out the solution.
Secondly, look at the below calculations to understand how the method of
multiplying the given number (150000) twice to get the population 2 years
ago is incorrect.
Method 1 - Suggested by Mr. Kanchwala:
Current Population (given) = 1,50,000
Population 2 years back = 1,36,054 (calculated as 1,50,000 / 1.1025)
Population 1 year back = 1,42,857 (calculated as 1,36,054 * 1.05)
Current Population = 1,50,000 (calculated as 1,42,857 * 1.05)
Method 2 - Suggested by Mr. Sharma:
Current Population (given) = 1,50,000
Population 2 years back = 1,35,375 (calculated as 1,50,000 * 0.95 * 0.95)
Population 1 year back = 1,42,144 (calculated as 1,35,375 * 1.05)
Current Population = 1,49,251 (calculated as 1,42,144 * 1.05)
Taking the calculated population 2 years back using the two methods, one
should be able to get the current population as given in the problem. This
does not happen in case of method 2 because 5% of 95 is not 5, it's 4.75.
Population 2 years back would be calculated as 0.9025x (0.95 * 0.95).
Population 1 year back would be 0.9025x + 0.045125x = 0.947625x and
current
population would be 0.947625x + 0.04738125x = 0.99500625x whereas it
should
be x.
The logic is simple - If you want to add 5% then multiply by 1.05 and if
you
want to subtract 5% then divide by 1.05.
Note that I am rounding off the numbers as population cannot be expressed
as
a decimal number,
Best Regards,
Zujar.
An optimist laughs to forget and a pessimist forgets to laugh!
-----Original Message-----
From: AccessIndia [mailto:accessindia-boun...@accessindia.org.in] On
Behalf
Of Mohib Anwar Rafel
Sent: Monday, June 24, 2013 10:21 PM
To: accessindia@accessindia.org.in
Subject: Re: [AI] help me in understanding the method for solving such
type
of mathematical problems
Thank you all.
On 6/24/13, Kartik Sawhney <sawhney.kar...@gmail.com> wrote:
Hi,
Rather than trying to understand the terminology, one can simply
understand the implication and complete the problem easily. For
instance, it isn't vital to understand the word `union`, and simply
understanding what it implies (either....or....both) is sufficient. So
basically, one can adopt an approach similar to the one in set theory,
without delving into its details as such. This way, the problems can
be approached a lot more efficiently in my view.
Best,
On 6/24/13, Vedprakash <vedprakash.sha...@gmail.com> wrote:
Yes, the set theory is easy but most of us have gone through mathes
up to tenth level.
That is why, the terms like a union b, or complementary etc., are new
to such aspirants.
----- Original Message -----
From: "Kartik Sawhney" <sawhney.kar...@gmail.com>
To: <accessindia@accessindia.org.in>
Sent: Monday, June 24, 2013 11:09 AM
Subject: Re: [AI] help me in understanding the method for solving
such type
of mathematical problems
Hi,
The solution as suggested by Mr. Sharma to 1B, is in fact, correct.
Accidently, Mr. Kanchwala has taken 150000 as 15000, resulting in
the anomaly.
Further, the solution to the second question as suggested is very
complecated. An easy way of approaching this is by employing set
theory.
Let h be the set of students who failed in Hindi, and E be the set
of students who failed in English Let the total No. of students in
the class=100 Now, we have:
No. of elements in H=35
No. of elements in E=45
Further, No. of elements in E intersection H=20 Further, we know:
E u H=No. of elements in e+No. of elements in H-No. of elements in e
intersection h Where u is union (You can learn this formula for this
type of problems, it will prove
handy)
Therefore, in this case:
e u h=35+45-20=60
Now, 60 students failed in either English or Hindi or both.
Therefore, students who did not fail in either of the subjects
(rather who passed in both the subjects)=100-60=40
Best,
On 6/23/13, Zujar Shabbir Kanchwala <zujarbri...@gmail.com> wrote:
Pardon me for addressing this post to the list.
I see that the solution suggested for question # 1b by Mr. S P
Sharma isn't correct and it needs be known to fellow list members
so that they can correct themselves. If one multiplies 15000 by 95%
twice to get the population 2 years back then the answer is 135375.
This answer is incorrect, the correct answer is 13605.
Here's the explanation:
Let x be the population 2 years back.
1 year back the population would be:
x + 0.05x
=1.05x
Current year the population would be:
1.05x + (0.05 * 1.05)x
=1.05x + 0.0525x
=1.1025x
Given that current year the population is 15000.
So, 1.1025x = 15000
Therefore, x = 15000 / 1.1025
=13605.44 rounded off to 13605.
Note that 5% of 100 is 5 but 5% of 95 is 4.75 not 5. So, if the
population
1
year back is 95 then current year it would be 95+4.75=99.75 and not
100.
The compound interest method suggested by Mr. Vedprakash fits in
best for such problems, it's shorter than the above method. I
mentioned the above method to explain how it works.
Hope this is clear...
Best Regards,
Zujar.
An optimist laughs to forget and a pessimist forgets to laugh!
-----Original Message-----
From: AccessIndia [mailto:accessindia-boun...@accessindia.org.in]
On Behalf Of Vedprakash
Sent: Sunday, June 23, 2013 11:25 AM
To: accessindia@accessindia.org.in
Subject: Re: [AI] help me in understanding the method for solving
such type of mathematical problems
Sorry for a wrong answer of the second question. sending the same
again.
2. In a class 35% students failed in hindi, 45% failed in english
subjects respectively. 20% students failed in both subjects, find
out the percentage of the students who passed in both subjects.
Total numbers of the students: = 100 Failed in Hindi = 35% Passed
in Hindi: = 100 minus 35 = 65.
Failed in English: = 45
passed in English = 100 minus 45 = 55.
failed in both = 20.
Passed in either Hindi or English = 100 minus 20 = 80.
Passed in Both =
A. Passed in either Hindi or English minus Passed in Hindi = 80
minus
65
=
15 Plus B. Passed in either Hindi or English minus Passed in
English
=80 minus 55 = 25
= A plus B
=15 plus25
=40 Answer.
----- Original Message -----
From: "Mohib Anwar Rafel" <mohibra...@gmail.com>
To: "accessindia" <accessindia@accessindia.org.in>
Sent: Saturday, June 22, 2013 9:34 PM
Subject: [AI] help me in understanding the method for solving such
type of mathematical problems
Hi friends I am unable to understand the way to solve the
following problems, even I couldn't understand it by reading R. S.
Agarwal book.
please guide me.
1. If the population of a town is 1,50,000 at present, it is
increasing at the rate of 5% per annum,
(a) what will be the population of the town after 2 years?
(b) what was the population of the town before 2 years?
2. In a class 35% students failed in hindi, 45% failed in english
subjects respectively. 20% students failed in both subjects, find
out the percentage of the students who passed in both subjects.
--
Mohib Anwar Rafel
M.Phil/Masters in International Law, Center for International
Legal Studies JNU.
Pursuing Masters of Law, at University of Delhi
Phone: 09811767506,
01127666896
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Studies
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Phone: 09811767506,
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