Discussion
In an examination, out of 480 students 85% of the girls and 70% of the boys passed. How many boys appeared in the examination if the total pass percentage was 75%?
Answer: C
The number of boys was 320.
Let \(b\) be the number of boys, so there are \(480 - b\) girls. The total number passing is 75% of 480, which is 360:
\[ \begin{aligned} 0.70b + 0.85(480 - b) &= 360 \\ 408 - 0.15b &= 360 \\ b &= \frac{48}{0.15} = 320 \end{aligned} \]
Check: 70% of 320 boys is 224 and 85% of 160 girls is 136, a total of 360. A quick alligation gives the same: the overall rate of 75% lies 5 points above 70 and 10 below 85, so boys and girls are in the ratio 10 : 5, or 2 : 1. 370, 340 and 360 do not split 480 in that ratio.
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