Question

Two consecutive even numbers are such that half of larger number exceed one- forth of smaller numbers by 5 .Then the large is​

Answer 1

Let the two consecutive even numbers be x, x + 2

Half of largest number = (x + 2)/2

One - fourth of smaller number = x/4

According to the question :

$\frac{x + 2}{2} - \frac{x}{4} = 5$

$\frac{2(x + 2) - x}{4} = 5$

$\frac{2x + 4 - x}{4} = 5$

$\frac{x + 4}{4} = 5$

x + 4 = 5 × 4

x + 4 = 20

x = 20 - 4

x = 16

Largest number = x + 2 = 16 + 2 = 18

Verification :

$\frac{18}{2} - \frac{16}{4} = 5$

9 - 4 = 5

5 = 5

LHS = RHS

So, my answer is correct.

Therefore the largest number is 18.