Question : In an examination out of 6000 students, 60% of boys and 90% of girls passed. If the total pass percentage was 65%, then what would be the number of boys?
Option 1: 3500
Option 2: 5000
Option 3: 4500
Option 4: 5500
Correct Answer: 5000
Solution :
Let the number of boys be $x$
The number of girls = 6000 – $x$
Now,
60% of $x$ + 90% of (6000 - $x$) = 65% of 6000
⇒ 0.6$x$ + 0.9(6000 – $x$) = 0.65 × 6000
⇒ 0.6$x$ + 5400 – 0.9$x$ = 3900
⇒ – 0.3$x$ + 5400 = 3900
⇒ – 0.3$x$ = – 1500
⇒ $x$ = $\frac{-1500}{-0.3}$ = $\frac{1500}{\frac{3}{10}}$ = $\frac{1500 × 10}{3}$ = 5000
Hence, the correct answer is 5000.
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