Transport of carbon dioxide

About 20-25% of $CO_2$ is indeed transported by haemoglobin as carbamino-haemoglobin (Assertion is true). This binding of $CO_2$ with haemoglobin is favoured by high $pCO_2$ and low $pO_2$, conditions found in the tissues (Reason is true and correctly explains the Assertion).

$CO_2$ is carried by the blood in three forms.
About 70 percent is carried as bicarbonate.
About 20 to 25 percent is carried by haemoglobin as carbamino-haemoglobin.
About 7 percent is carried in a dissolved state in the plasma.
At the tissues, $CO_2$ diffuses into the red blood cells, where the enzyme carbonic anhydrase catalyses the reaction $CO_2 + H_2O \rightleftharpoons H_2CO_3 \rightleftharpoons HCO_3^- + H^+$
In the alveoli, where the partial pressure of $CO_2$ is low, the reaction proceeds in the opposite direction and $CO_2$ is released.
So the majority of the carbon dioxide is transported as bicarbonates.