Two numbers are in ratio 7:9, and their sum is 128. Find the numbers.

Question

Two numbers are in ratio 7:9, and their sum is 128. Find the numbers.

1. A. 49, 79
2. B. 56, 72 (Correct answer)
3. C. 62, 66
4. D. 70, 58

Correct Answer

Option B — 56, 72

Detailed Solution & Explanation

The correct answer is 56, 72.

Key Points

• Let the numbers be 7x and 9x, matching the ratio 7 : 9.
• Their sum is 16x = 128, so x = 8.
• The numbers are 7 × 8 = 56 and 9 × 8 = 72.

Additional Information

• Check both conditions: 56 + 72 = 128 ✓ and 56 : 72 simplifies to 7 : 9 ✓. Distractors usually satisfy the sum but not the ratio.
• Option A (49, 79) sums to 128 but is not in 7 : 9 — exactly that trap.
• The general method: express the parts as multiples of a common factor, solve for the factor, then substitute back.

प्रश्न (हिन्दी में)

दो संख्याएँ 7:9 के अनुपात में हैं, और उनका योग 128 है। संख्याएँ ज्ञात कीजिए।

1. A. 49, 79
2. B. 56, 72
3. C. 62, 66
4. D. 70, 58