Question

Given below are two quantities named A and B. Based on the given information, you have to determine the relationship between the two quantities. You should use the given data and your knowledge of Mathematics to choose between the possible answers.

Quantity A: A class has two sections A and B in an examination 40% of students of section A failed. section B has 200% more students than section A, and overall 56.25% of the students passed the examination. Find the percentage of students of section B who failed the examination.  

Quantity B: 60%

1. Quantity A > Quantity B
2. Quantity A < Quantity B
3. Quantity A ≥ Quantity B
4. Quantity A ≤ Quantity B
5. Quantity A = Quantity B or No relation

Answer 1

Correct Answer - Option 2 : Quantity A < Quantity B

GIVEN:

Fail % of section A = 40%

Students in B= 300% of students in section A

Overall pass percentage = 56.25%

EXPLANATION:

Let total students in section A be x.

failed students in Section A = 40% of x = .4x

Students in Section B = 300% of x = 3x

Total students = x + 3x = 4x

Number of students failed = 43.75% of 4x = 1.75x

Number of students failed in section B = 1.75x - .4x = 1.35x

% of failed students in section B = 1.35x/3x × 100 = 45%

∴ Quantity A < Quantity B

ALTERNATE SOLUTION:

Overall fail % = 43.75

Let x% students failed in section B

                                A             B

F% →                     40            x

 

overall F%→               43.75

 

Students(Ratio)→   1               3

∴ 43.75 - 40 = 3 ratio

⇒ 1 ratio = 1.25

43.75 + 1ratio = x

⇒ x = 45%

∴ Quantity A < Quantity B