Multiple choice

On the occasion of teacher's day, some number of boys and girls contributed some money. The average contribution of boys was Rs. 250 and that of girls was Rs. 100. If the average contribution per student was Rs. 160 on the whole then what percent of students are boys?

  1. 60%

  2. 44%

  3. 40%

  4. 80%
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let B be number of boys, G be number of girls. 250B + 100G = 160(B+G). 250B + 100G = 160B + 160G. 90B = 60G. B/G = 60/90 = 2/3. Boys as percentage of total = 2/(2+3) = 2/5 = 40%.

AI explanation

Using the method of alligation, the overall average contribution is Rs. 160, the boys' average is Rs. 250, and the girls' average is Rs. 100. The difference between the boys' average and the overall average is 90, and the difference between the overall average and the girls' average is 60. This gives a ratio of boys to girls of 60 to 90, or 2:3, meaning out of 5 total parts, 2 parts are boys. The percentage of boys is therefore (2/5) * 100, which is 40%.

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