Final answer:
The ratio of seniors taking only Igbo to those taking only Hausa is calculated by subtracting the number of students taking both languages from each group, resulting in 80 seniors taking only Igbo and 60 taking only Hausa. The simplified ratio of students taking only Igbo to only Hausa is 4:3.
Step-by-step explanation:
To find the ratio of the number of seniors taking only Igbo to the number taking only Hausa, we must first determine how many are taking only one of these languages. If 100 seniors are taking Igbo and 20 of these are also taking Hausa, then the number of seniors taking only Igbo is 100 - 20 = 80. Similarly, if 80 seniors are taking Hausa and 20 of these are also taking Igbo, then the number taking only Hausa is 80 - 20 = 60.
Now, we can make a ratio of the two quantities. The ratio of the number of students taking only Igbo to the number of students taking only Hausa is 80:60. To simplify this ratio, we divide both numbers by their greatest common divisor, which is 20. Doing that, we get 4:3. However, this ratio is not listed in the provided options, indicating there might have been an error in the question or the options provided.