In a class of 40 students, the average marks of the boys are 62 and the average marks of the girls are 72. The average marks of the whole class are 66. Which of the following statements are correct?
(A) The ratio of the number of boys to the number of girls is \(3 : 2\).
(B) There are 16 girls in the class.
(C) The total marks of the boys are 1488.
(D) The total marks of the girls are 1200.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (A), (B) and (C) only
The class average 66 is the mean of the two group averages, so the rule of alligation gives the ratio of the group sizes.
\(\text{Boys} : \text{Girls} = (72 - 66) : (66 - 62) = 6 : 4 = 3 : 2\)
\(\displaystyle \text{Boys} = \frac{3}{5} \times 40 = 24\)
\(\text{Girls} = 40 - 24 = 16\)
\(\text{Total marks of boys} = 24 \times 62 = 1488\)
\(\text{Total marks of girls} = 16 \times 72 = 1152\)
So there are 24 boys and 16 girls, with total marks 1488 and 1152.
Checking the statements
(A) The ratio of the number of boys to the number of girls is \(3 : 2\). — Correct. \(24 : 16 = 3 : 2\).
(B) There are 16 girls in the class. — Correct. \(40 - 24 = 16\).
(C) The total marks of the boys are 1488. — Correct. \(24 \times 62 = 1488\).
(D) The total marks of the girls are 1200. — Incorrect. \(16 \times 72 = 1152\).