In an exam one student get 25% marks and falls by 30 marks. Another student get 40% which is 60 more than the passing mark. Find the passing percentage

Questions : In an exam one student get 25% marks and falls by 30 marks. Another student get 40% which is 60 more than the passing mark. Find the passing percentage?

Answer:  

Shortcut Rule for Passing Marks Calculation

We can use the formula:

$$\text{Passing Marks} = \frac{\text{Difference in Marks}}{\text{Difference in Percentage}} \times \text{Lower Percentage} + \text{Failing Difference}$$

Applying the Formula

Given:

• First student scored 25% and failed by 30 marks.
• Second student scored 40%, which is 60 marks more than passing marks.
• Difference in percentage = 40% - 25% = 15%.
• Total difference in marks = 30 + 60 = 90.

Now, using the formula:

$$P = \frac{90}{15} \times 25 + 30$$ $$P = 6 \times 25 + 30$$ $$P = 150 + 30 = 180$$

Finding Passing Percentage

$$\frac{180}{600} \times 100 = 30\%$$

Thus, the passing percentage is 30%, calculated quickly using the shortcut!

Additional Techniques 

Here's how to solve this problem:

1. Set up variables:

   • Let 'P' be the passing marks.
   • Let 'T' be the total marks.

2. Create equations based on the given information:

   • Student 1: 0.25T = P - 30 (25% of total marks is 30 less than passing marks)
   • Student 2: 0.40T = P + 60 (40% of total marks is 60 more than passing marks)

3. Solve the system of equations: We can solve for 'T' and 'P' using substitution or elimination. Here's one way using elimination:

   Subtract the first equation from the second equation:

   (0.40T - 0.25T) = (P + 60) - (P - 30)

   0.15T = 90

   T = 90 / 0.15

   T = 600

4. Substitute T back into one of the equations to find P: Let's use the first equation:

   0.25 * 600 = P - 30

   150 = P - 30

   P = 150 + 30

   P = 180

5. Calculate the passing percentage:

   Passing percentage = (P / T) * 100

   Passing percentage = (180 / 600) * 100

   Passing percentage = 30%

Answer: The passing percentage is 30%.

CBSE / NCERT / SAT/ UPSC 

You Can Translate It In Your Language :-

  EDUTICAL

Mock Test Click Here

Maddhamik Previous Year Solution Click Here

CBSE CLASS 10 History Notes Click Here

If you like this content, please CLICK any of the Ads In This Page.

Thank you 

Team EDUTICAL