A cell of emf 6.0 V and negligible internal resistance is joined to a resistor of 24 Ω…

Step 1. Without the meter. $I_0 = \dfrac{6.0\ \text{V}}{24\ \Omega} = 0.250\ \text{A}$.

Step 2. With the meter. The resistances add in series: $24\ \Omega + 2.0\ \Omega = 26\ \Omega$. So $I = \dfrac{6.0\ \text{V}}{26\ \Omega} = 0.231\ \text{A}$.

Step 3. The error. $\dfrac{I_0 - I}{I_0} = \dfrac{0.250 - 0.231}{0.250} = 0.077$, that is $7.7\ \%$.

Step 4. The limit. The error is $\dfrac{I_0 - I}{I_0} = 1 - \dfrac{R}{R + R_A} = \dfrac{R_A}{R + R_A}$. We want this below $0.01$. So $R_A < 0.01(R + R_A)$, and $R_A < \dfrac{0.01 \times 24\ \Omega}{0.99} = 0.242\ \Omega$.