If the ratio of two numbers is 3:5 and their sum is 64, find the numbers.

Question

If the ratio of two numbers is 3:5 and their sum is 64, find the numbers.

1. A. 24, 40 (Correct answer)
2. B. 20, 44
3. C. 18, 46
4. D. 16, 48

Correct Answer

Option A — 24, 40

Detailed Solution & Explanation

The correct answer is 24, 40.

Key Points

• Let the numbers be 3x and 5x, so 3x + 5x = 8x = 64 and x = 8.
• The numbers are 3 × 8 = 24 and 5 × 8 = 40.
• Check: 24 + 40 = 64 and 24 : 40 simplifies to 3 : 5 ✓.
• With a ratio and a sum, divide the sum by the total number of parts — here 64 ÷ 8 — to get one part instantly.
• The same one-part method handles any ratio problem with a stated total: divide by the sum of the ratio terms, then scale each part.
• If instead the difference were given — say the numbers differ by 16 — you would divide by the difference of the terms (5 − 3 = 2), not their sum.

Additional Information

• With a ratio and a sum, divide by the sum of the ratio terms; with a ratio and a difference, divide by their difference instead.
• Ratios can be scaled freely: 3 : 5 is the same relationship as 24 : 40, which is why checking the simplified form verifies an answer instantly.
• The same one-part method underlies partnership, alligation and age problems, so it is worth making automatic.

प्रश्न (हिन्दी में)

यदि दो संख्याओं का अनुपात 3:5 है और उनका योग 64 है, तो संख्याएँ ज्ञात कीजिए।

1. A. 24, 40
2. B. 20, 44
3. C. 18, 46
4. D. 16, 48