In a class of 80 students and 20 teachers, each student got sweets which was x% of total number of students, while every teacher got sweets which was 2x% of total no. of students. If some sweets were also donated to homeless, whose number was equal to 50% of the sweets given to the all the teachers, then what is the value of ‘x’, if 560 sweets were bought in total?
Correct Answer: Option E
⇒ No. of sweets given to each student \(= \frac{x}{{100}} \times 80\)
⇒ Total no. of sweets given to students \(= \left( {\frac{x}{{100}} \times 80} \right) \times 80 = 64x\) ___________(1)
⇒ No. of sweets given to each teacher \(= \frac{{2x}}{{100}} \times 80\)
⇒ Total no. of sweets given to all teachers \(= \left( {\frac{{2x}}{{100}} \times 80} \right) \times 20 = 32x\) ___________(2)
⇒ No. of sweets donated to homeless = 32x/2 = 16x ___________(3)
According to the question,
⇒ Equations (1) + (2) + (3) = 560
Solving the above equations we get,
⇒ ‘x’ = 5
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