Question: 1. A certain number of student from school X appeared in an examination and 30% student failed. 150% more students than more from school X, appeared in the same examination from school Y, If 80% of the total number of students who appeared from X and Y passed, then what is the percentage of student who failed from Y? (a) 24 (b) 20 (c) 16 (d) 18
1. **State the problem:**
We have two schools, X and Y. From school X, 30% of students failed. School Y has 150% more students than school X. Overall, 80% of students from both schools passed. We need to find the percentage of students who failed from school Y.
2. **Define variables:**
Let the number of students from school X be $x$.
Then, the number of students from school Y is $x + 1.5x = 2.5x$.
3. **Calculate students who passed and failed from X:**
Failed from X = $30\%$ of $x = 0.3x$
Passed from X = $70\%$ of $x = 0.7x$
4. **Calculate total students and total passed:**
Total students = $x + 2.5x = 3.5x$
Total passed = $80\%$ of total students = $0.8 \times 3.5x = 2.8x$
5. **Calculate passed from Y:**
Passed from Y = Total passed - Passed from X = $2.8x - 0.7x = 2.1x$
6. **Calculate failed from Y:**
Total students from Y = $2.5x$
Failed from Y = Total Y - Passed Y = $2.5x - 2.1x = 0.4x$
7. **Calculate percentage failed from Y:**
$$\text{Percentage failed from Y} = \frac{0.4x}{2.5x} \times 100 = \frac{0.4}{2.5} \times 100 = 16\%$$
**Final answer:** The percentage of students who failed from school Y is **16%**.
This corresponds to option (c).