The total number of students (science + commerce) over five years from 2012 to 2016 is 2400. The percentage distribution of total students over these years is as follows:

![image.png](https://res.cloudinary.com/aptidude/image/upload/v1755941828/aptidude_questions/jvnsj9smghyzudcowg7x.png)

Note: Commerce students in 2013 are 8 less than those in 2015.

What is the difference between the number of commerce students in 2016 and the number of science students in 2012 expressed as a percentage of the total students in 2013?

Question

The total number of students (science + commerce) over five years from 2012 to 2016 is 2400. The percentage distribution of total students over these years is as follows:

![image.png](https://res.cloudinary.com/aptidude/image/upload/v1755941828/aptidude_questions/jvnsj9smghyzudcowg7x.png)

Note: Commerce students in 2013 are 8 less than those in 2015.

What is the difference between the number of commerce students in 2016 and the number of science students in 2012 expressed as a percentage of the total students in 2013?

Accepted Answer

**Solution:**

1. Calculate total students for each year using the given percentages of total 2400 students:
   - 2012: $2400 	imes 0.38 = 912$
   - 2013: $2400 	imes 0.20 = 480$
   - 2014: $2400 	imes 0.10 = 240$
   - 2015: $2400 	imes 0.03 = 72$
   - 2016: $2400 	imes 0.04 = 96$

2.![image.png](https://res.cloudinary.com/aptidude/image/upload/v1755942043/aptidude_questions/wo0ziyd75xh3svb9wnm1.png) Calculate commerce students for each year using the given percentages:
   - 2012: $912 	imes 0.25 = 228$
   - 2013: $480 	imes 0.30 = 144$
   - 2014: $240 	imes 0.16 = 38.4$
   - 2015: $72 	imes 0.15 = 10.8$
   - 2016: $96 	imes 0.14 = 13.44$

3. Check the note: Commerce students in 2013 are 8 less than in 2015.
   - From above, 2013 commerce = 144, 2015 commerce = 10.8, which contradicts the note.

This indicates the initial percentages given for total students and commerce students might be inconsistent with the note.

4. Using the data table provided:
   - Total students in 2012 = 480
   - Science students in 2012 = 280
   - Commerce students in 2012 = 200

- Total students in 2013 = 240
   - Commerce students in 2013 = 112

- Commerce students in 2015 = 120

Note says commerce students in 2013 is 8 less than in 2015:
   - 120 - 112 = 8 (matches the note)

5. Commerce students in 2016 = 128
   Science students in 2012 = 280

6. Find the difference:
   $$128 - 280 = -152$$
   Since difference is negative, take absolute value: 152

7. Calculate the percentage of this difference with respect to total students in 2013:
   $$\frac{152}{240} 	imes 100 = 63.33\%$$

**Answer:** 63.33\%

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