Work done by Rakesh, Prakash and Ashok

Let efficiencies be $r, p, a$. Total work $W = r + p + a$. Also $W = p(1) + a(4) = p + 4a$. Equating: $r + p + a = p + 4a \implies r = 3a$.

Let time taken by Prakash be $t$ hours. Time by Rakesh = $t-1$ hours. $W = p \cdot t = r(t-1) \implies t = \frac{r}{r-p}$. Also $p \cdot t = p + 4a \implies t = 1 + \frac{4a}{p}$.

Substituting $r = 3a$ and $a/p = k$: $\frac{3k}{3k-1} = 1 + 4k \implies 12k^2 - 4k - 1 = 0 \implies k = \frac{1}{2}.$ So $p = 2a$.

Total Work $W = 3a + 2a + a = 6a$. Time taken by Ashok alone = $\frac{6a}{a} = 6$ hours.