Aptitude - Percentage - Discussion

Discussion :: Percentage - General Questions (Q.No.15)

15. 

The population of a town increased from 1,75,000 to 2,62,500 in a decade. The average percent increase of population per year is:

[A]. 4.37%
[B]. 5%
[C]. 6%
[D]. 8.75%

Answer: Option B

Explanation:

Increase in 10 years = (262500 - 175000) = 87500.

Increase% = 87500 x 100 % = 50%.
175000

Required average = 50 % = 5%.
10


Manisha said: (Nov 17, 2010)  
how to solve this question if 20% of man's salary is paid as rent, 60%are his living expanses, and 10% is paid in L.I.C. if he spends remaining Rs. 30 on the education of the children, find his salary.

Aparna said: (Jan 28, 2011)  
@manisha
suppose his salary is Rs.100
20% of 100=20
100-20=80
60% of 80=48
80-48=32
10% of 32=3.2
32-3.2=28.8

hence
28.8 = 30
100 =?

we get
104.16
hence his salary is Rs.104.16

Vijay said: (Apr 28, 2011)  
@aparna you may be wrong becoz...

suppose his salary is x Rs.
then 20% of his x for rent=20/100*x = 20x/100...1
60% of his x for living expanses = 60x/100...2
10% of his x for LIC = 10x/100...3
30 Rs on education he spent

then we can write (20x/100)+(60x/100)+(10x/100)+30 = x
solve this you get x = 300
for check you put x value in all equations 1,2, 3 and add them with 30
you get total salary as 300

Rahul said: (May 31, 2011)  
@vijay.

Ya you are right vijay. Watt aparna did is wrong.

Vishnu said: (Jun 10, 2011)  
Ya vinay is right.

Let his salary is x. let us consider only expenses (20/100)*x+(60/100)*x+(10/100)*x are expenses.
in problem it given that if we subtract all expenses from salary,he remained with 30rs which used for education so,
x-((20/100)*x+(60/100)*x+(10/100)*x)=30
(100x-(20x+60x+10x))/100=30
100x-90x=3000
10x=3000
x=300
so vijay is right.......of course me tooooo.

Naren said: (Jun 23, 2011)  
Ya vijay is correct....

Let his expenses 20+60+10=90

Remaining money 30, means 10%=30, Then 100%=300

Muthupazhani said: (Jun 25, 2011)  
No need to do these much calculation its very simple
consider his salary is X then
give 10% of his salary is 30rs from this
x*10/100=30
x/10=30
x=300

Pavan said: (Jun 29, 2011)  
Nice Muthupazhani.

Jagadeesh said: (Jul 20, 2011)  
What is required average? Why it is divided by 10?

Reeta said: (Nov 26, 2011)  
What is required average? Why it is divided by 10?

Suman said: (Dec 3, 2011)  
Thanku Naren you gave a very shortcut method.

Shivani said: (Feb 4, 2012)  
@ jagadeesh and reeta

1 decade = 10 years ........

here we need the average of percent rise ...

here the increment in percentage for 10 years is 50

so average = 50 / 10
= 5

got it?? ....

Bhavna said: (Jul 6, 2012)  
Thanks shivani.

Ak123 said: (Aug 17, 2012)  
Why is 87,000 divided by 1,75,000? can someone explain.

Bluespark said: (Aug 20, 2012)  
@ak123
%increase=(increase*100)/year its a formula since u r finding the increase % of 175000, yr=175000

Niks said: (Aug 24, 2012)  
By the way aparna's answer to manishas question is right. How can you reuse the total amount be it rs 100 or x again and again. Plus I have seen a lot of similar examples solved it in aparnas way. Check out for these kind of examples in MBA aptitude books.

Prasad. said: (Sep 6, 2012)  
Easy method to find the salary of the person.
20% on rent+60%on living +10% on L.I.C.+ remain 30rs on children.
20%+60%+10%+30rs=100%.
90% spent remain 30rs is equal to 10%. (.i.e 100%-90%=10%)
if 10 % =30rs ==> 100%=300 Rs.

Sheshu said: (Dec 9, 2012)  
%increase=difference/lowvalue*100.

%decrease=difference/highvalue*100.

Sree said: (Sep 19, 2013)  
How far the answer 5% is correct.

(50/10)% is OK but on back_end process the value(262500) cannot satisfy 175000.

If 4.137% suits for it.

CAN ANYONE UNDERSTOOD?

CAN ANYONE HEAR TO CLEAR MY DOUBT?

Rajesh said: (Jan 11, 2014)  
Hai @Sree.

First I assume your answer is correct, now 4.137% in first year means answer increase of 7240, now I 175000+7240= 182240(this value is the population up to 2nd year, now I add 4.137% of 18220..

This process is continued so that I will get the answer of the population at the end of 12th year,

But this the wrong of doing, here you are calculating the increase in percentage of the next year w.r.t to previous year (for example you are calculating the 3rd year increase in percentage of the population of 2nd year, this gives the result wrong as per our question, here in our question they asked the avg increase in % )...hope you understand.

Udhaya Kumar said: (Jun 18, 2014)  
Which of the following multipliers will cause a number to be increased by 29.7%?

Answer is 1.297.

Please anybody solve this and clear me this problem.

Akhil Nair said: (Sep 27, 2014)  
@Udhaya Kumar:

Let's say that the number is 100.

Now increase in 29.7 % means.
100+29.7%100 = (100+29.7) = 129.7-----> (1).

Now the multiplier is 1.297. So multiply it to the assumed number i.e.
100*1.297=129.7-----> (2).

So from (1) & (2) the number increased by 29.7%.

Hope this helped.
Have a nice test !

Ravi said: (Oct 5, 2014)  
Population of town is increased by 5% annually. If its population in 2001 was 138915. What it was in 1998? reply soon.

Sunil said: (Nov 26, 2014)  
1,20,000 is the right answer.
138915 = X(1+5/100)^(10).
Calculate X = 1,20,000.

Mahi said: (Jan 30, 2015)  
Why we use 10 here?

Sunil Vishwakarma said: (Feb 10, 2015)  
10 is because there is formula of 2 years, p(1+r/100)^t, where t is for next 2 year, is 2*5 = 10.

Yatender said: (Feb 22, 2015)  
Most of them are wrong because firstly we use our original salary then 20%of that salary=remaining and 60% of that remaining and so on. @Aparna is right.

Dinesh said: (Jul 5, 2015)  
Dear @Manisha you can solve that problem very simply.

Add all the expenses so 20+60+10 = 90.

Out of 100% 90% spending on his expenses so 100-90 = 10.

Let the salary be x.

10% of x = 30.
10/100*x = 30 we get.

1/10*x = 30.
So x = 300.

Aparna said: (Jul 21, 2015)  
How 50/10 came in the last step. Can anyone help me to understand?

Anil said: (Aug 17, 2015)  
Two numbers are respectively 25% and 20% more than of third. What percentage is the first of second. Could you solve this problem any one?

Saravanan said: (Aug 25, 2015)  
How to say it's 10 years difference?

Shashi said: (Aug 25, 2015)  
Dear, @Anil.

What is the third number?

Sneha said: (Sep 6, 2015)  
May be it is:

a-0.25 x = c.
b-0.20 x = c.

a-0.25 x = b-0.20 x.
a-0.45 x = b.
a is 45% greater than b.

Samuelaa said: (Oct 19, 2015)  
If a number is 20% more than the other, how much percent is less than the first?

Can somebody solve this please?

Vikrala said: (Feb 4, 2016)  
There's a shortcut here i.e 100*r/100+r = 100*20/100+20.

You can easily get the result.

Shivaranjitha said: (Jun 27, 2016)  
Maybe, if the 3rd no = 100.

Then 1st no is 25% more than that = 125.

In the same way 2nd no=120.

Now the question is 125 is What % of 120.

So it would be (125/120) *100.

Approximately equal to 104.

Ashok said: (Jun 28, 2016)  
@Manisha.

10% = 30rs(given).

Then,
20% = 60rs (30 * 2 = 60, 10 * 2 = 20%).

Similarly;

60% = 180rs,
10% = 30rs,

Add all gives 100% = 300rs.

Agentsteel said: (Jul 1, 2016)  
20 + 60 + 10 = 90%,

Rem 10% = 30,

Therefore, total salary = 300.

Rajesh said: (Jul 10, 2016)  
Why 175000 is taken in the denominator instead of taking 2,62,500?

Swathi said: (Aug 3, 2016)  
@Rajesh.

The question says to find out the Avg. Percent of increase per year. 17500 is the initial population which the place had hence you can't take the increased population, ie, 263500 because you Have to find the increase only. So 175000 is the denominator.

Mathu said: (Aug 5, 2016)  
Why we can't use 262500. To divide the number 87500.

Keshav said: (Aug 11, 2016)  
@Aparna,

20% + 60% + 10% = 90%.

Means rest 10% = 30 rupee.

So obviously his salary will be 300 (100%).

Aman said: (Aug 13, 2016)  
Population of town is increased by 5% annually. If its population in 2001 was 138915. What it was in 1998.

In this question what is the formula?

@Sunil I don't know where you derive your formula.

Angelo said: (Aug 13, 2016)  
What is the answer, if the population of the town is increased by 5% annually. If its population in 2001 was 138915. Then What was it in 1998?

Please anyone solve this.

Sreekanth said: (Aug 26, 2016)  
Anyone explain how 50/10?

Surya said: (Sep 23, 2016)  
Decade means?

Ann said: (Oct 12, 2016)  
I think the official answer is wrong : if you increase a population of 175,000 by 5% each year during 10 years it becomes more than 262,500.

Proof 175,000 * (1.05 ^ 10) = 285'056.56 that's more then 262,500!

So it should be less than 5%.

Right answer : ( (262,500/175,000) ^ 0.1) - 1 = 4.137974%.

So, A mus be the right choice.

Mohsin said: (Oct 23, 2016)  
10% is equal to 30.

While 100% is equal to?
Then,
30 * 100/10 = 300.

Satwika said: (Nov 6, 2016)  
Why should we take 17,5000 in denominator why not 26,25000?

Shru said: (Nov 13, 2016)  
Guys it's very simple, here they used the formula for % change that is =difference in % ÷ initial value * 100.

Arisha said: (Nov 17, 2016)  
How (50/10)%?

Anil said: (Nov 23, 2016)  
Population in 2001 = 138915
Population in 1998 was = 138915 * 100/105 * 100/105 * 100/105 = 1,20,000.

Had it given the population in 1998 = 1,20,000 then what will be the population in 2001, if it increases @5% PA.

The solution would be = 1,20,000 * 105/100 * 105/100 * 105/100 = 138915 (population in 2001).

Krishnam Raju said: (Dec 24, 2016)  
percentage increase = (increased quantity/initial quantity) * 100.

As given above problem.

Increased quantity = 262500 - 17500.
= 87500
Percentage increase = (87500/175000) * 100.
= 50% per decade means for 10 years.

Per one year = 50/10 = 5%.

Jayakumar S said: (Apr 16, 2017)  
In an election between two candidates, 75% of the voter's caste their votes, out of which 2% of the votes were declared invalid. A candidate got 9261 votes which were 75% of the total valid votes. Find the total number of votes enrolled in that election.

Can anyone solve this?

Sankarilakshmi said: (Apr 21, 2017)  
Hi @Jayakumar s

let the total number of votes = x
no.of votes cast = 75% of x
The valid votes = 98% of (no.of votes cast)
i.e 98% of (75% of x) (here 2% is invalid so (100-2)%=98%)

Then (A candidate got 75% of valid votes =9261)
75% of (98% of (75% of x) = > 75/100 * 98/100 *75/100 * x =9261.
= > (9261*100*100*100) / (75*98*75),
= > 9261000000 / 551250,
= >16800.

Nikhil Dasari said: (May 5, 2017)  
We can also solve with options.

A) 4.37 % 175000 = 7647.5.
So decade means 10 year.
multiply 10*7647.5= 76475.
and add the multiply result with the 175000.
i.e)76475+175000 =2514755% 17500.
So it's not matching.

B) 5% 175000 = 8750.
so decade means 10 year.
multiply 10*8750= 87500.
and add the multiply result with the 175000.
i.e)87500+175000 = 262500.

Its right so answer is B.

Amreen said: (May 12, 2017)  
Percentage formula.

% = [final value-intial value/intial value] * 100.
% = 87500/17500 * 100.
= 5 is the ans hence proved.

Mr. Bhatiya said: (Aug 5, 2017)  
Good @Shivani.

Anil said: (Aug 9, 2017)  
Why we divided 50 by 10?

Lopamudra said: (Dec 24, 2017)  
Suppose man's salary =100 Rs.

20%=20 Rs rent,
60% =60 Rs Expense,
10% =10 Rs LIc,
so left amount for education=100-(20+60+10)=10,
10% left ie 10 Rs of 100 %,
10%= 30(In qs),
1% =30/10,
100% =30*100/10=300(salary).

Saiswarupa said: (May 11, 2018)  
Thank you @Nikhil Dasari.

Nagesh N said: (Aug 26, 2018)  
Fresh fruit contains 68% water and dry fruit contains 20% water. How much can dry fruit be obtained from 100 kg of fresh fruits?

Please answer this.

Suman Debnath said: (Sep 17, 2018)  
Increase in 10 years =(262500 - 175000) = 87500.

Increase % in 10 years = (175000 * x/100)%,
x= 50%.

In 1 year = (50/10)%.
Ans = 5.

Rekha said: (Feb 13, 2019)  
But there was not mentioned exactly 10 years. Can you please explain how it came?

Ganeshvictory said: (Mar 7, 2019)  
1 decade = 10 years.

Population increased as 175000 to 262000 in decade;
x = (262000-175000) = 87500.
increase percentage =(x/175000*100) = 50%.
The required average of decade from increased percentage = [increased percentage / decade] = (50/10)% = 5%.

Ajit Raj said: (Mar 17, 2019)  
@Manisha.

Take total salary = 100%.
100% - 20% - 60% - 10%,
= 10%.

According to the question:
10%= 30, then,
100%=x,
By cross multiplication, we got x= 300.
Which was his total salary.

Shakil said: (Mar 21, 2019)  
It's like compound interest. Here, Every year more people are coming into existent. so we need to count interest rate on increased capital. Formula for compound interest is:

Increased capital = initial capital(1+rate)^year.

Bunny said: (May 2, 2019)  
Why you take (50/10)%?

Sanjana said: (May 11, 2019)  
@Bunny.

Here,
1 decade = 10 years
Therefore, to find out the increased average percentage for( per year) would be always divided by 10. That's why 50 which is increased Percentage is then divided by 10 to find out the increased average percentage for PER YEAR!

Prince said: (May 15, 2019)  
But using the formula we get the answer is 4.137.

Ravi Kumar said: (Aug 24, 2019)  
Hello @Manish.

Total will be 100%
20% for rent.
60%for expenses.
10% for LIC.
TOTAL 90% OVER.
Know remaining spend 30.
10%=30 then 100%=300 total salary.

Riad said: (Oct 6, 2019)  
Suppose,
Salary = x.

(100-90)% of x = 30.
10/100 * x = 30.
x = 30*100/10.
x = 300.

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