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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? 
1. 50%
2. 30%
3. 40%
4. 45.55%

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Correct Answer - Option 4 : 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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