Question

In 2020, a certain number of students for institute A appeared in the annual examination and 35% o the students failed. In the same year, 250% more students than that of A appeared in the same examination from institute B. If 70% of the total students of A and B_{1} passed the examination, then the fail percentage o students of institute B is​

Answer 1

Given:

Percentage of passing student in school A = 65%

Percentage of passing student in school A and B = 75%

Compared to school B 100% more students appeared in school A.

Calculation:

Let the number of student be in school A is Y and number of passing student in school B is P%

Percentage of passing student in school A = Y × 65%

Percentage of passing student in school A = Y × (65/100)

Total number of student in school B = 2Y

Percentage of passing student in school B = 2Y × P%

Percentage of total number of passing student in school A and B = (Y + 2Y) × 75%

⇒ Y × 65% + 2Y × P% = (Y+ 2Y) × 75%

⇒ Y × (65/100) + 2Y × (P/100) = (3Y) × (75/100)

⇒ 2Y × (P/100) = (225Y/100) – (65Y/100)

⇒ 2Y × (P/100) = (160Y/100)

⇒ 2Y × (P/100) = (160Y/100)

⇒ (P/100) = (80/100)

⇒ P = 80

Percentage of failed student in school B = 100% – 80%

Percentage of failed student in school B = 20%

∴ The percentage of failed student in school B is 20%

Shortcut Trick

Let the Total number of student be in school A is 100 and the failed student in school B is Q%

Percentage of Failed student in school A = 100 × 35%

Percentage of Failed student in school A = 100 × (35/100)

Percentage of Failed student in school A = 35

100% more students than those in school A, appeared in the same examination from school B.

⇒ Total number of student in school B = 100 × (200/100)

⇒ Total number of student in school B = 200

⇒ Total number of student in school A and B = (100 + 200)

⇒ Total number of student in school A and B = 300

Total number of student who failed in school A and B = 300 × 25%

⇒ 100 × 35% + 200 × Q% = 300 × 25%

⇒ 100 × (35/100) + 200 × (Q/100) = 300 × (25/100)

⇒ 35 + 2 × Q = 75

⇒ 2Q = 40

⇒ Q = 20

∴ The percentage of students who failed in school B is 20%