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The sum of two numbers is 42 and one of them exceeds the other by 18. Find the greater number.
32
24
28
30
30
To find the greater number, use the formula: (Sum + Difference) / 2. Here, (42 + 18) / 2 = 60 / 2 = 30.
Sum of two numbers = 42, difference between the two numbers = 18
x+y=42, x−y=18
To find the greater number, use the formula: (Sum + Difference) / 2. Here, (42 + 18) / 2 = 60 / 2 = 30.
Students often calculate the smaller number (42 - 18) / 2 = 12 instead of the greater number.
Define variables
Let the greater number be x and the smaller number be y. We are given the sum and the difference.
x+y=42, x−y=18
Add the equations
Add the two equations to eliminate y: (x+y)+(x−y)=42+18
2x=60
Solve for x
Divide both sides by 2 to find the greater number x.
x=260=30
D is correct because the greater number is calculated as 30 by solving the simultaneous equations.
This type of basic algebraic system is foundational for ratio and proportion problems in competitive exams where you often solve for individual quantities given their aggregate relationships.
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