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There are 5 colleges in university `XYZ’ namely A, B, C, D and E. The number of students in college A is 25% of the total number of students in University ‘XYZ’. The number of students in college C is 60% of the number of students in college A. The number of students in college D is three fourth of the number of students in college C. The number of students in college E is 1/2 the number of students in college C. The number of students in college E is 450.
In college A, the total number of teachers is 1/20 th of the total number of students. If the total number of teachers in college C is 15 less than the total number of teachers in college A, what is the total number of teachers in college C ?
Let the total number of students in all colleges together = $$100x$$
=> Number of students in A = $$\frac{25}{100} \times 100x = 25x$$
Number of students in C = $$\frac{60}{100} \times 25x = 15x$$
Number of students in college D = $$\frac{3}{4} \times 15x = \frac{45x}{4}$$
Number of students in E = $$\frac{1}{2} \times 15x = 7.5x = 450$$
=> $$x = \frac{450}{7.5} = 60$$
Number of teachers in college A = $$\frac{1}{20} \times 1500 = 75$$
=> Number of teacher in college C = $$75 - 15 = 60$$
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