The sum of two numbers is 176 and their difference is 16. What is the ratio of the two numbers?

Correct option is A

Given:

• Sum of two numbers = 176
• Difference of two numbers = 16
• Required: Ratio of the two numbers

Concept Used:

Let the two numbers be x and y, where x > y.

Then:

• x + y = 176
• x − y = 16

Add and subtract the equations to find x and y.

Solution:

Step 1: Add the two equations:

x + y = 176
x − y = 16
———————
2x = 192 => x = 96

Step 2: Use x to find y:
x + y = 176 => 96 + y = 176 => y = 80

Step 3: Ratio of the two numbers:
96 : 80

Divide both by 16:

96 ÷ 16 = 6
80 ÷ 16 = 5

So, the ratio is 6 : 5

Final Answer: (A) 6 : 5