If p, q, r, be three positive numbers such that p > q > r when the smallest number is added to the difference of the rest two numbers, then…

We know that, formula for average:

⇒ $(\left\{ {{A_E} = \frac{{{S_E}}}{{{n_E}}}\;or\;{S_E} = {A_E} \times {n_E}} \right\})$

where,

SE = Sum of entities,

nE = Number of entities,

AE = Average of entities.

Now, according to the question:

$(\frac{{\left[ {r + \left( {p - q} \right)} \right] + \;p + q}}{3} = 21 + \frac{{p + q + r}}{3})$

$(\Rightarrow \frac{{2p + r}}{3} - \;21 = \frac{{p + q + r}}{3})$

$(\Rightarrow \frac{{p - q}}{3} = 21)$

⇒ p – q = 63

∴ T$he required value of (p - q) is 63