Final answer:
To calculate the number of students taking only Hausa, subtract the 20 students taking both languages from the 80 students taking Hausa to get 60 students. Then, find the ratio of students taking only Hausa to the total number taking a language, which simplifies to 3:8.
Step-by-step explanation:
To find the ratio of the number of students taking only Hausa at Police Secondary school, we start by identifying the total number of students taking Hausa, which is 80. Since 20 students are taking both Igbo and Hausa, to find the number taking only Hausa, we subtract the number taking both from the total number taking Hausa.
80 (total Hausa students) - 20 (students taking both) = 60 students taking only Hausa.
There is no need to consider the number of students taking only Igbo since it does not affect the ratio we are looking for. The question asked specifically for the number of students taking only Hausa. Therefore, the ratio of students taking only Hausa to the total number of students taking a language is 60:160 (100 Igbo + 80 Hausa - 20 Both) or, when simplified, 3:8.