An ammeter of resistance R give a full scale deflection when a...

Given, resistance of the ammeter is $R$.

Full scale deflection current, $I_g = 3\ \text{A}$.

Maximum current to be measured, $I = 10\ \text{A}$.

Let the required shunt resistance be $S$.

Since the shunt is connected in parallel with the ammeter, the potential difference across both will be the same.

$I_g R = (I - I_g) S$

$3 \times R = (10 - 3) \times S$

$3R = 7S$

$S = \dfrac{3R}{7}$

Answer: $3R/7$