Question

The difference of two numbers is 780 and their sum is 1120. Then the larger number is

• A. 880
• B. 900
• C. 950
• D. 975

Hint:

Add equations when sum and difference are given to directly find the larger number.

Answer 1

The Correct Option is C

The problem involves finding two numbers given their difference and sum. Let's denote the two numbers as a and b, with a being the larger number.

1. According to the problem statement, the difference of the two numbers is 780. Therefore, we have:

\(a - b = 780\)

1. We are also given that the sum of the two numbers is 1120, which can be expressed as:

\(a + b = 1120\)

1. Now, we have a system of two equations:
   1. \(a - b = 780\)
   2. \(a + b = 1120\)
2. To find the value of a, we can add these two equations:

\((a - b) + (a + b) = 780 + 1120\)

\(2a = 1900\)

1. Solving for a, we divide both sides by 2:

\(a = \frac{1900}{2} = 950\)

1. Thus, the larger number is 950.

This verifies the given correct answer as 950. The alternative options are incorrect, as substituting them into the equations would not satisfy both the given sum and difference.