Question

Students in a commerce class took a test. The average score of men is 70 and of women is 83. The class average is 76. What is the ratio of men to women in the class?

• A. 6:7
• B. 7:6
• C. 7:8
• D. 8:7

Answer 1

The Correct Option is B

To solve this problem, we need to find the ratio of men to women in the class based on their average scores and the overall class average.

1. The average score of men is given as 70.
2. The average score of women is given as 83. 
3. The class average score is given as 76.
4. Let's assume the number of men in the class is \(M\) and the number of women is \(W\).
5. The total score for men will be \(70M\) and for women, it will be \(83W\).
6. The total score for the class is also given by the formula for average, which is:
   \(\frac{70M + 83W}{M + W} = 76\)
7. Expand and simplify the equation:
   \(70M + 83W = 76(M + W)\)
8. Distribute the 76 on the right-hand side:
   \(70M + 83W = 76M + 76W\)
9. Rearrange the terms to form:
   \(83W - 76W = 76M - 70M\)
   \(7W = 6M\)
10. Divide both sides by 6:
    \(\frac{W}{M} = \frac{6}{7}\)
11. Therefore, the ratio of men to women \(\left(\frac{M}{W}\right)\) is:
    \(\frac{7}{6}\)

Hence, the correct answer is that the ratio of men to women in the class is 7:6, which matches option

7:6

.