Seats for Mathematics, Physics, and Biology are in the ratio 5 : 7 : 8. If they are increased by 40%, 50%, and 75% respectively, what is the ratio of the increased seats?

Problem restatement
Apply percentage increases to a ratio and express the new counts in simplest ratio form.

Given data

• Original ratio (Math : Physics : Biology) = 5 : 7 : 8.
• Increases: 40% (M), 50% (P), 75% (B).

Concept/Approach
Multiply each term by its growth factor (1 + rate) and then simplify the resulting ratio.

Step-by-step calculation
New M = 5 × 1.40 = 7.00 New P = 7 × 1.50 = 10.50 New B = 8 × 1.75 = 14.00 Ratio = 7 : 10.5 : 14 = multiply by 2 → 14 : 21 : 28 Simplify by 7 → 2 : 3 : 4

Verification/Alternative
Any common scalar multiple (e.g., 14 : 21 : 28) is equivalent; simplest form is 2 : 3 : 4.

Common pitfalls

• Adding percentages directly to the ratio numbers (e.g., 5+40) instead of scaling by the correct factor.

Final Answer
2 : 3 : 4