In an examination, out of 480 students, 85% of girls and 70% of boys pass. How many boys appeared for the examination, if the total pass percentage of the examination is 75%?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 320
The number of students who passed can be counted in two ways: as 75% of all 480 students, and as the girls who passed plus the boys who passed. The two counts must be equal, which gives the number of boys.
Boys \(=x\), so girls \(=480-x\)
Students who passed \(=75\%\) of \(480=360\)
Girls who passed + boys who passed: \(0.85(480-x)+0.70x=360\)
\(408-0.85x+0.70x=360\), so \(408-0.15x=360\)
\(0.15x=48\), so the number of boys \(x=320\)
Shortcut: The pass rate of all the students, 75%, is a mixture of the girls’ 85% and the boys’ 70%, so alligation gives the ratio of girls to boys at once.
Girls : boys \(=(75-70):(85-75)=5:10=1:2\)
Boys \(\displaystyle =\frac{2}{3}\times480=320\)