Multiple choice

In a school the average score of all 1400 students at an examination was found to be 69.5 The average score of boys in the school was 68 and that of girls was 72 Hence the number of boys and the number of girls respectively are

  1. $680$ and $720$
  2. $720$ and $680$
  3. $875$ and $525$
  4. $800$ and $600$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let B be boys and G be girls. B + G = 1400. 68B + 72G = 69.5 * 1400 = 97300. Substitute G = 1400 - B: 68B + 72(1400 - B) = 97300. 68B + 100800 - 72B = 97300. -4B = -3500. B = 875. G = 525.

AI explanation

Using the method of alligation, the ratio of boys to girls is (72 minus 69.5) to (69.5 minus 68), which is 2.5 to 1.5 or 5 to 3. Since the total number of students is 1400, one unit equals 1400 divided by 8, which is 175. Therefore, the number of boys is 5 multiplied by 175 to give 875, and the number of girls is 3 multiplied by 175 to give 525.

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