Question

Male and female students from a particular subject took a class test. The average score of male students was 70 and of female students was 83. The class average however was 76. Determine the ratio of males to females in the class ?

• A. 8:7
• B. 6:7
• C. 7:8
• D. 14:17
• E. 7:6

Hint:

Alligation shortcut: Male deviation from mean $= 76-70=6$; Female deviation $= 83-76=7$. Ratio males:females $= 7:6$ (cross-multiply deviations). Always cross-multiply in alligation.

Answer 1

Answer: (E)

Step 1: Understanding the Concept:
Use the alligation method or weighted average equation to find the ratio.

Step 2: Detailed Explanation:
Let males $= m$, females $= f$. $\frac{70m + 83f}{m+f} = 76$. $70m + 83f = 76m + 76f$. $83f - 76f = 76m - 70m$. $7f = 6m$. $\frac{m}{f} = \frac{7}{6}$. Ratio males:females $= 7:6$.

Step 3: Final Answer:
The ratio of males to females is 7:6.