Question

Find two consecutive even numbers such that the difference of one-half the larger number and two-fifths the smaller number is equal to five.

38 and 40
40 and 42
42 and 44

Answer 1

40 and 42..................

Answer 2

The correct option is 2. The consecutive even numbers are 40 and 42.

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.

`(1)/(2)(x+2)-(2)/(5)(x)=5`

`(x+2)/(2)-(2x)/(5)=5`

`(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.