D
$\text{Time} = \frac{\text{Distance}}{\text{Speed}}$
So, $\frac{d}{v_K}= \frac{d-10}{v_A}$
$\implies v_K=\frac{10v_A}{9}$
in 2nd race
$\frac{d+10}v_K=\frac{d}{v_A}$
$\frac{d+10) 9}{10v_A}=\frac{d}{v_A} \\ \implies 9d + 90 = 10d \\\implies d = 90$
So, they meet at a distance of 90m and since Karan runs faster, he reaches the destination first. So naswer must be D. Still to confirm we can do
$\frac{110}{v_K} = \frac{d}{v_A} \\ \implies \frac{110 \times 9}{10v_A} = \frac{d}{v_A} \\\implies d = 99$.
So, Karan wins Arjun by $100 - 99 = 1m.$