We have given :

gas mixture made up of 

A_r - 10g

CO₂ - 14.2 g

K_r - 32.1 g

Volume of mixture of gases = 24.5 L

Temperature = 260°C or 533 K

Number of moles of A_r = \(\cfrac{10.0}{39.948}\) = 0.25 mole

Number of moles of K_r = \(\cfrac{32.1}{83.79}\) = 0.38 mole

Number of moles of CO₂ \(\cfrac{14.2}{44}\) = 0.32 mole

Total number of mole of gases = 0.32 + 0.38 + 0.25

= 0.95 mole

assume, the mixture of gases follow ideal gases equation 

PV = nRT

= P = \(\cfrac{0.95}{24.5L}\) x 0.082 x 533

= 1.7 atm

mole fraction of A_r = \(\cfrac{0.25}{0.95}\) = 0.26

mole fraction of K_r = \(\cfrac{0.38}{0.95}\) = 0.40

mole fraction of CO₂ = \(\cfrac{0.32}{0.95}\) = 0.34 

partial pressure of A_r = (P_Ar) =  mole fraction x total pressure at A_r

= 0.26 x 1.7 atm

= 0.442 atm

partial pressure of K_r (P_kr) = 0.40 x 1.7 atm 

= 0.68 atm

partial pressure of CO₂  = (CO₂) = 0.34 x 1.7 atm

= 0.578 atm

Hence, The total pressure of mixture of gases will be 1.7 atm and partial pressure of A_r, K_r and CO₂ will be 0.442 atm, 0.680 atm and 0.578 atm respectively