Answer:
The correct option is 2. The consecutive even numbers are 40 and 42.
Step-by-step explanation:
Let the two consecutive even numbers be x and x+2.
It is given that the difference of one-half the larger number and two-fifths the smaller number is equal to five.
\(\frac{1}{2}(x+2)-\frac{2}{5}(x)=5\)
\(\frac{x+2}{2}-\frac{2x}{5}=5\)
\(\frac{5x+10-4x}{10}=5\)
\(x+10=50\)
\(x=50-10\)
\(x=40\)
The value of x is 40. Therefore the two consecutive even numbers are 40 and 42.
Option 2 is correct.
