Aptitude - Percentage - Discussion

Dear @Chandan it is very simple,

Two students total mark in percentage is 56% that mention in the question.

If we discuss this line the result is x+y = 56%.

But the question says one of them secured 9 marks than other.

So we assume one student is (x+9) and other is x.

Here x+9 means x+9 is secured 9 marks extra than x.

Now if we try to find out the value of x from x+9. If we find out the x output then we must find out both students mark.

x+9 = 56(x+9+x)/100 [here we write 56(x+9+x) means both students percentage is 56%].

x+9 = 14(x+9+x)/25.
25(x+9) = 14(2x+9).

3x = 99 [25x+225 = 28x+126 => 28x-25x = 225-126 =>3x = 99].

x = 33[x = 99/3 => 33].

Now the original output is:

Two students are: x, (x+9).

1st student's mark is: x = 33.

2nd student is secured 9 marks than 1st student => (x+9) = 33+9 = 42.

Output option is C: 42, 33.

Let's say two students are X and Y.

For instance, assume that the total mark was 100. Meaning X+Y = 100.

Now, if X gets 56% of the sum of their marks which was 100, then Y must have the remaining percentage of the marks, that's 44%.

Now, compare the difference between the marks that they've obtained and the percentage that they have.

So, difference in percentage = X-Y = 56-44 = 12%
And, the difference in marks = X-Y = 9 (Because in the question it's given that one has 9 marks more than the other.)

Now, we've to find the value of 1 Unit. If you can find that you can easily solve the question.

Comparing their marks and their percentages,

12% = 9 marks.
1 Unit = 9/12.
1 Unit = 0.75.

Now multiply the value of 1 Unit by the percentage they've got.

X = 56*0.75 = 42.
Y = 44*0.75 = 33.
And their difference is also 9.

Understand the statement :

One of them secured 9 marks more than the other.
So it is (9 + x) , right ?

Next part is " 56% of the sum of their marks"
So here, sum is (x + 9 + x).
And its 56% is (56/100) * (x + 9 + x).

So now, the important part is " .. 9 marks more than the other AND HIS MARKS WAS 56% of ... "

In this line, it says HIS Marks, so whose marks it is ?? It is the marks of ( 9 + x ).
(9 + x ) is the 56% of their sum.

Because of this line, we have equal to symbol in the equation,

So the equation is : (9 + x) = (56/100) * (x + 9 + x).

A simple Answer.

Here given 2 students (assume A&B)
* One of the student(A) marks is = 56%
* And remaing student (B) marks is =44% (100%-56%)
Then, the gap between them is=12% (56-44).

So we know that one person got more marks than another person = 9mrks.

So,
A.
12%-----------> 9mrks.
56%----------> ?
Then {56*9/12}.
Ans 42.

Similarly for B;
12%-------> 9mrks
44%-------> ?
=> {44*9/12} = 33.

very 1 stape is just to calculate total marks in each option,
suppose, I'm choosing 39 30 then total marks are 69 which is 100% if u calculate 56% of 69 i.e 56*69/100 you get 38.64 which is not in option. so leave it there.

if you're taking 42 33 then total marks are 75 which is 100% and 56% of 75 is 42 hence option C is correct.

though it is lengthy procedure, we can choose the option for calculation by little thinking before solving it.

First find total marks

difference between percentage=56%-44%=9%

In the question given difference between marks as 12

so, if mark is percentage

9 12%

? 100%

so by cross multiplying total marks=(9*100)/12=75.

now student 1s marks=56% of 75 i.e

(56/100)*75=42.

student 2s marks=44% of 75 i.e

(44/100)*75=33.

Please, don't confuse with these calculations, my advice is to go by options because, we have two exam marks.

And in question they have asked about the 56% of sum of two exam marks. So go by this way.

Check options:

1. 56/100*69 = 38.
2. 56/100*73 = 40.88.
3. 56/100*75 = 42.
4. 56/100*77 = 43.12.

So the option 3 answer matches with the option 3 in the question. The correct answer is option 3. i.e.. 42, 33.

Explain it.

In an exam, 5%of the application were found ineligible &85% of the eligible candidates belongs to general category. If 4275 eligible candidates belonged to other categories, then how much candidates applied for the exam?

90% application is a general category and ineligible. So balance 10%are other categories and it's 4275 application. So 10%is equal to 4275 then 100% is equal to 42750 application.

@All.
I have a solution.
56% = 56\100 = 14\25.
Let's take the total mark = 25.
The higher scorer's mark = 14.
The lower scorer's mark =25 - 14 = 11
The difference given in the question is 9 so,
14parts - 11parts = 9,
value of 3 parts = 9,
so the value of 1 part = 9\3= 3.

Now we have to calculate higher scorer's marks = 14 * 3 = 42.
Then we have to calculate the lower scorer's marks = 11 * 3 = 33.

@Aniket.

Let total mark be x.

50% of x--> (50/100)*x = (1/2)x

Therefore (1/2)x-100 = P --(1). Here P is the pass mark.

70% of 1st candidate marks--> 70% of (1/2)x
(7/20)x.

Therefore (7/20)x+50 = P --(2).

Then equating (1) and (2) we get,
(1/2)x-100 = (7/20)x+50 ==> 3x = 3000.
x = 1000.

Then 50% of x
(50/100)*1000 = 500.

500-100 = 400;
400 is the Answer.