Two numbers are in the ratio 3 : 4 and their sum is 420. What is the greater of the two numbers?

Introduction / Context:
When a sum and a ratio are known, each part equals the sum divided by the total number of parts. Multiply the unit part by the appropriate ratio component to obtain each number.

Given Data / Assumptions:

• Ratio = 3 : 4
• Sum = 420
• We want the larger number (the “4” part).

Concept / Approach:
Total parts = 3 + 4 = 7. Each part (unit) = 420 / 7. Then greater number = 4 * (unit part).

Step-by-Step Solution:
Unit part = 420 / 7 = 60Greater number = 4 * 60 = 240

Verification / Alternative check:
Smaller number = 3 * 60 = 180. Sum check: 180 + 240 = 420 (correct ratio and total).

Why Other Options Are Wrong:
175, 200, and 315 do not align with 3:4 and total 420; 180 is the smaller number, not the greater.

Common Pitfalls:
Using 420/4 directly and ignoring the ratio; swapping the 3-part and 4-part accidentally.

Final Answer:
240