According to the question

Sum of two numbers = x+y=18  ---Eq(1)

Four times of one = 4x

and five times the other number = 5y

Now, 4x-5y=0  ---Eq(2)

From Eq(1) we get,

⇒  x+y=18

⇒ x=18-y

Substitute 'x' in Eq(2) we get,

⇒ 4(18-y)-5y=0

⇒ 72-4y=5y

 ⇒ -4y-5y=-72

 ⇒ -9y=-72   [divide both sides by '-9']

we get,

 ⇒ y=8

Substitute 'y' value in Eq(2) we get,

 ⇒ 4x=5×(8)

 ⇒ 4x=40

 ⇒ x=10

∴ x=10, y=8

The bigger of the two number is x=10

Hence, option C is correct.