
Shortcut Trick
Let the number of boys be 50 and girls be 70, making the total number of students 120.
Boys without scholarships = 60% of 50 = 30.
Girls without scholarships = 50% of 70 = 35.
Total students without scholarships = 30 + 35 = 65.
Required percentage = (65 ÷ 120) × 100 = 325 ÷ 6 = 54 1/6%.
∴ The correct answer is 54 1/6%.

Alternate Method
Given:
Ratio of Boys to Girls = 5 : 7
Boys getting scholarships = 40%
Girls getting scholarships = 50%
Formula Used:
Percentage = (Favorable Value ÷ Total Value) × 100

Calculations:
Let the number of boys be 5x and the number of girls be 7x.
⇒ Total students = 5x + 7x = 12x
Since 40% of boys get scholarships, those who do not get scholarships = (100 − 40)% = 60%
⇒ Number of boys without scholarships = 60% of 5x = (60 ÷ 100) × 5x = 3x
Since 50% of girls get scholarships, those who do not get scholarships = (100 − 50)% = 50%
⇒ Number of girls without scholarships = 50% of 7x = (50 ÷ 100) × 7x = 3.5x
⇒ Total students without scholarships = 3x + 3.5x = 6.5x
⇒ Required percentage = (6.5x ÷ 12x) × 100
⇒ (65 ÷ 120) × 100 = 1300 ÷ 24 = 325 ÷ 6 = 54 1/6%
∴ The correct answer is 54 1/6%.

Additional Information
Percentage Base Assumption
When working with ratios and percentages, assuming bases as multiples of 10 or 100 eliminates decimals and speeds up calculations significantly.
Complementary Percentage
If a certain percentage (P%) satisfies a condition, the remaining (100 − P)% does not. Directly calculating the required part saves an extra subtraction step.
Weighted Average
The combined percentage of multiple groups is essentially their weighted average: Combined % = (n1p1 + n2p2) ÷ (n1 + n2).