Aptitude - Percentage - Discussion

@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.

Let the marks of the first student be x.

Then, the other student got x + 9 marks.
Total marks = x + (x + 9) = 2x + 9,
Given: x + 9 = 56% of (2x + 9),
=> x + 9 = 0.56(2x + 9),
=> x + 9 = 1.12x + 5.04,
=> -0.12x = -3.96,
=> x = 33,

So, the other student got 33 + 9 = 42.
Answer: 33 and 42 marks.

Your explanation is simple & clear. Thank you very much @Neelu.

Let the marks obtained by the students be a and b:

Let a = b + 9 -------->1
a = (56/100) * (a+b) ---------> 2.

From equation 1, equation 2 can be written as;

b + 9 = (0.56) * (b + 9 + b),
b + 9 = (0.56)(2b + 9).
b + 9 = 1.12b + 5.04
9 - 5.04 = 1.12b - b.
3.96 = 0.12b,
b = 3.96/0.12,
b = 33.

Then, a=b+9
a=33+9
a=42

Therefore, marks scored by a and b are 42 and 33.

Simple way using ratio.

56 : 44.
i.e 14:11.
33 is divisible by 11 so the answer is C.

Why we Equalize 56/100 (2x+9) into x+9? can anyone please explain this?

Total 100%.

A have 56%.

i.e B = 100%-56% = 44%.
A have 9 mark more than B,
i.e A - B=9.
56% - 44%=9,
12% = 9,
4% = 3.

A = 56% / 4% = 14%.
14 * 3 = 42.
B = 44 %/4%
B = 11 * 3 = 33.

so, A = 42, B = 33.

25(x+9) = 14(2x+9),
25x + 234 = 28x + 126,
25x - 28x = 126 - 234,
3x = 108,
x = 108/3,
x = 33,
y = 33 + 9 = 42.

Thanks all for giving an excellent explanation.

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.