Arithmetic

Percentages

Medium

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 %?

320

370

340

360

✅ Correct Option: 1

Total students = 480

Girls' pass rate = 85%

Boys' pass rate = 70%

Overall pass rate = 75%

Total students who passed = 75% of 480

$= \frac{75}{100} \times 480$

$= 360$ students

Let the number of boys = $B$

Let the number of girls = $G$

Total students:

$G + B = 480$ ... (1)

Students who passed:

70% of boys passed = $0.70B$

85% of girls passed = $0.85G$

Total who passed = 360

$0.85G + 0.70B = 360$ ... (2)

From equation (1):

$G = 480 - B$

Substituting into equation (2):

$0.85(480 - B) + 0.70B = 360$

$408 - 0.85B + 0.70B = 360$

$408 - 0.15B = 360$

$0.15B = 408 - 360$

$0.15B = 48$

$B = \frac{48}{0.15}$

$B = 320$

Therefore, 320 boys appeared for the examination.

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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 %?

Solution

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