Two numbers are in the ratio 4 : 5. If their HCF is 16, what is the sum of these two numbers?

Question

Two numbers are in the ratio 4 : 5. If their HCF is 16, what is the sum of these two numbers?

1. A. 144 (Correct answer)
2. B. 124
3. C. 165
4. D. 157

Correct Answer

Option A — 144

Detailed Solution & Explanation

The correct answer is 144.

Key Points

• This question uses the key property that when two numbers are in a ratio a : b in their lowest terms, their HCF (Highest Common Factor) is the common multiplier.
• The numbers are in the ratio 4 : 5 and their HCF is 16, so the two numbers are:
• 4 × 16 = 64 and 5 × 16 = 80.
• Their sum = 64 + 80 = 144.
• Verification: HCF(64, 80) = 16 ✓ and 64 : 80 = 4 : 5 ✓.
• if two numbers = a·H and b·H where H is the HCF and a, b are co-prime, then sum = (a + b)·H and product = a·b·H².
• Here sum = (4 + 5) × 16 = 9 × 16 = 144.

Exam Tip

• this shortcut — sum = (ratio total) × HCF — instantly solves HCF-ratio questions without listing the actual numbers.