Your competence with percentages and its application should form a very important part of your armory of CAT 2010 preparation or, for that matter, preparation for any other MBA exam. The concept of percentage will be applied in not only your quant section but also your data interpretation (DI) section. Therefore, master this important concept and make it your habit to calculate percentages mentally.

 
The word "percentage" literally means "per hundred" or "for every hundred." Therefore, whenever you calculate something as a part of 100, that part is numerically termed as percentage.

In other words, percentage is a ratio whose second term is equal to 100. For example, 1:4 can be written as 25: 100 or 25%, 3: 8 can be written as 37.5: 100 or 37.5%, 3: 2 can be written as 150: 100 or 150%, and so on.

IMPORTANT CONCEPTS ASSOCIATED WITH PERCENTAGE

Basic formula of percentage:

Percentage of:

Percentage increase/decrease:

Percentage increase/decrease when a quantity a increase/decreases to become another quantity b is
 

Percentage less than/greater than:

Have a look at the picture given below:

You can see that Johnny is taller than Vicky. What will your answer be if I ask

(a)      By what percentage is Johnny taller than Vicky?

(b)      By what percentage is Vicky shorter than Johnny?

Answer:

Therefore, to find the final quantity after a 20% increase, we can directly multiply the old quantity by a factor of 1.2 and get the new quantity. Similarly, for a 20% decrease, we can multiply the old quantity by 0.8 and get the new quantity. The factors to be multiplied for various percentage increase/decrease are given below:

The biggest advantage of using the factors is that for subsequent percentage increase/decrease, we just keep on multiplying the corresponding factors and get the final quantity.

Example:

1.       The performance bonus of a salesman increases by 10% in the first year, by 20% in the second year, and by 30% in the third year. What is the overall percentage increase in his bonus in 3 years?

Answers: Let the bonus at the start of the first year be Rs100.

Therefore, to find the final bonus we just multiply by factors.

Final bonus = 100 Ã— 1.1 × 1.2 × 1.3 = 171.6.

Therefore, overall percentage increase = 71.6%

 
NOTE: note that taking initial value of 100 makes the problem simpler; whatever increase we get is directly equal to the percentage increase.

2.       An amount was first reduced by 10% and then further reduced by 20% and Rs10 800 were left. What was the original amount?

Answer: Let the original amount be A.

Therefore A × 0.9 (factor for 10% decrease) × 0.8 (factor for 20% decrease) = 10 800

Or A = Rs15 000.

·        SOME SOLVED EXAMPLES

I shall have to end here and leave the rest of it for my CBT Club students. I shall cover some problems based on this in the CBT Club this week.

If you think this article was useful, help others by sharing it with your friends!

Hi tg,

Thanks a lot.. ur approach is too good.

Dear TG Sir,

In the watermelon question, it says 30g of water evaporated, which has reduced the percentage of water from 85% to 80% i.e, a reduction of 5%

5% of water is 30g.

85% of water would be 510g.

15% was solid matter i.e, 90g.

So, total 600g.

What is the fallacy in this question ?

hi tg.i have a doubt.please help.

Q. If a merchant offers a discount of 40% on the marked price of his goods and thus ends up selling at cost price, what was the % mark up?

of the adult population in NAGPUR ,45 % of men and 25 % of women are married .Wht percentage of the total population of adults is married (assume that no man marries more than one women and vice versa )

???

 Hi , Nikhil

 I think these assumptions are valid  in california only.  i will stick to the fact that no. of married males = no. of married females.

Re:

Thanks TG for making concept more clear but I would recomment to use some very tough problems which requires use of multiple concepts

I came across one of the question,plz help me to sort it out.

The radius of a circle is 21 cm,find the % of the numeric value of area to the numeric value of its radius.

I came across one of the question,plz help me to sort it out.

The radius of a circle is 21 cm,find the % of the numeric value of area to the numeric value of its radius.

o.6 M.p= c.p
M.p/c.p =5/3
Mp-cp/cp=2/3
Mp is 66.67% of cp

...on the above question...i have a comment on the last part - > Mp is 66.67% of cp,,,as m.p/c.p=5/3 ; so m.p is 166.66% of c.p...that means m.p is 66.67% greater than c.p...

thanks

Sibu

Hi Sinha..

             Even the questions are not asked to me ; but I put my explanations in below....

1) If the number is x ; then Hursh's wanted/right  value is x-5 , but the mistake/wrong value x+5.

so total change = (x+5)-(x-5)=10

so percentage change will be 10*100/(x-5) %...(let x=25 , then percentage change will be 10*100/20 %= 50 %....)

2) Do this problem by percentage change grph.....let  the quantity of hematite mined 100.

then 100 (by 20% of the ore get wasted ..that will be 80 )-----------80.........(25 % of 80 will be pure iron ; so it will be 20)--------20

If  pure iron obtained in a year from a mine of hematite was 80000kg then
    the quantity of hematite mined from that mine in the year is =100*80000/20=4,00,000 kg....(ans)

3) Let total no of student 100...and no of student pass for both =x% ;

then (80-x)+(70-x)+x+15 = 100 (if you draw the ven diagram then u can find this easily...)...

so x= 65 % ...now this 65 % of total student  =325

then no of total student = 100*325/65= 500 (ans...)

Hi Sinha

           let me think the  question.4...

Thanks

Sibu

Hi Rahul is it the ratio of the  october salary  to his salary for november  15:1.333  or 1.5:1333 , please let me know?

Hi All,

A method which I use to solve the problems of type 'Solved Example 1'.
 In this problem price increase by 10%, or we can say by '1/10'.
Therefore the decrease in consumption would be
1/(10+1) = 1/11 = 9.09%.

In other words if price( or any other value for that matter) increase by "a/b" then the subsequent decrease in cosumption would be "a/(b+a)".
After we get a fraction we need to convert it into a percentage using the table given by TG.

Ofcourse this would become a little complicated if the value of the fraction calculated is not found in the table.

Now say the value of decreases, then what would be the increase in consumption.
This can also be calculated as follows:
Suppose the value decreases by 37.5%, i.e. 3/8.
then the consumption would increse by '3/5' or 60%.

In other words if the value decreases by 'a/b', then the consumption would be increased by 'a/(b-a)'.
Notice that b will always be greater than a. This is so because the decrease can never be equal to or greater than 100%.

I had devised these formulae while studying percentages, so I thought it would be nice to share these with fellow TGites. Hope you liked these.

Thanks and Regards,
IO.

Sorry

my mistake....

its (1.5) : (1.333)

Thank you!!!

For question (1) i have answer with me as 33.33% as per book( Need to verify it again)

2) and 3) are correct clear to me.

For 3) can you please let me know how did you write the expression                                      (80-x)+(70-x)+x+15 = 100

I know it but just i wanted to make sure whether my thinking over that is correct or not.

Thank you

Rahul

Hi TG's

Few questions:  i am having problem while solving it

1)If the length , breath and height of a cube are decreased, decreased  and increased by 5%, 5% and 20%
 respectively, then what will be the impact on the surface area of the cube(in % term)?

2)The minimum quantity of milk in liters(In whole numbers) that should be mixed in a mixture
  of 60ltr in which the initial ration of milk to water is 1:4 so that the resulting mixture
  has 15% milk is

Regards,

Rahul

Hi Rahul

     For your clarification of the equation (80-x)+(70-x)+x+15 = 100  (for your question no 3) ; I just give u an example...

let total student 10 ; out of 10 student 5 student pass in Physics , 4 pass in Math, 2 fail; if in this case 2 ( let x)  pass in both subject then pass only in Physics  5-2 =3; pass only in Math  3-2=1; pass in both subject =2 ( x) ;  fail 4 ; then your equation will be ==(5-2) + (3-2)+2 + 4 =10..

thanks

Soln

1) Let 'a' be the side of the cube..
The new length and breath would be '0.95a' and height would be '1.2a'.
Now initial surface area is 6(a^2).
New surface area wud be : 2[ (0.95a)*(0.95a) + (1.2a)*(0.95a) + (1.2a)(0.95a)]
= 2 [ 0.9025 (a^2) + 2.28 (a^2) ]
= 6.365 (a^2)

Therefor increase %age = 0.365/6 *100 = 6.0833%

2) In this problem, solution already has 20% milk. So by adding milk we will only increase the %age and not decrease it. I guess your question is wrong.

Thanks and Regards,
IO

Hi Rahul Sinha,

Is the answer for the 4th question you have posted (Salary & Bonus question) Rs. 295/- approx. ?????

Let me know whether it's correct.

Rgds,

Suren

yes the ans z  in 2pprs..

one of d solutions can b lyk...

its given dt,d ratio for total marks z 1:1:2:2

for simplicity,lets assume the marks as 250,250,500  n 500.

agn d ratio of obtained marks z 4:8:13:15

dis ratio can b writn as 120:240:390:450(multipling d ratio term 4:8:13:15 by 30)

ie;the obtained marks are 120/250,240/250,390/500 n 450/500

which means only 2 of them,240/250 n 450/500 r abv 80%.

this solution also satisfies the condition that he got 80% of marks in total(as the total marks r 1500(250+250+500+500)n marks obtained r 1200(120+240+390+450)).

hence d ans dt he gets abv 80%marks in two sbjcts...

ok...nw i understood...

n thts a very good approach indeed...

I feel there is a typo error in the explanation given for percentage increase/decrease.
It has been highlighted below in BOLD style.

--------------------------------------------------------------------------------Percentage increase/decrease when a quantity a increase/decreases to become another quantity b is

Where , [(a-b)/a]*100 when a<b (decrease)  should be
        [(a-b)/a]*100 when b<a (decrease)

-------------------------------------------------------------------------------------

hi mohit..ans) 72%

exp;-sushant=1080 implies mohitz=1296 now using percentage knowledge we know 10% less means 11.11% more which is 1/9 in frction..thereby 1/9 * 1296=144 to be added to 1296 gives 1440 rajeshz marks!!!!!...so 72 %...hope its clear...

Arsh Arora

Hi TG,

Request you to please write on Ratio & Proportions. It would be of great help.

Thanks