The volume ($V$) of a monatomic gas varies with its temperature ($T$), as shown in the graph (a straight line passing through the origin). The ratio of work done by the gas, to the heat absorbed by it, when it undergoes a change from state A to state B, is:

The graph shows a straight line passing through the origin in the $V-T$ plane, which implies $V\propto T$. According to the ideal gas law $PV=nRT$, if $V/T$ is constant, the pressure $P$ must be constant. Thus, the process is isobaric.Work done ($dW$) in an isobaric process is given by:
$$dW=PdV=nRdT$$
Heat absorbed ($dQ$) in an isobaric process is given by:
$$dQ=n{C}_{p}dT$$
For a monatomic gas, $C_p=\frac{5}{2}R$.The required ratio is:
$$\frac{dW}{dQ}=\frac{nRdT}{n{C}_{p}dT}=\frac{R}{C_p}$$
$$\frac{dW}{dQ}=\frac{R}{\frac{5}{2}R}=\frac{2}{5}$$