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Ratio of number of boys and number of girls eligible for the scholarship test is 4 ∶ 5. If 60% of eligible boys and 50% of eligible girls attend the test, find the percentage of students who did not attend the exam? 

Ratio of number of boys and number of girls eligible for the scholarship test is 4 ∶ 5. If 60% of eligible boys and 50% of eligible girls attend the test, find the percentage of students who did not attend the exam?  Correct Answer 45.55%

Given:

Ratio of number of boys and number of girls eligible for the scholarship test is 4 ∶ 5.

60% of eligible boys and 50% of eligible girls attend the test.

Concepts used:

Percentage of eligible students who did not attend the test = Number of eligible students who did not attend the test/Total number of eligible students × 100

Calculation:

Ratio of number of boys and number of girls eligible for the scholarship test is 4 ∶ 5. 

Let the number of eligible boys be 4x and number of eligible girls be 5x.

60% of eligible boys and 50% of eligible girls attend the test.

⇒ Number of eligible boys who attended the test = 60% of 4x = 12x/5

⇒ Number of eligible girls who attended the test = 50% of 5x = 5x/2

Total number of boys and girls who attended the test = 12x/5 + 5x/2

⇒ 49x/10

Number of eligible boys and girls who did not attend the test = (4x + 5x) - 49x/10 

⇒ 41x/10

Percentage of eligible students who did not attend the test = Number of eligible students who did not attend the test/Total number of eligible students × 100

⇒ Percentage of eligible students who did not attend the test = (41x/10)/9x × 100

⇒ 45.55%

∴ 45.55% of the total eligible students did not attend the scholarship test.

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