Equivalent weights of carbon in CO and ${\mathrm{CO}}_2$ respectively are in the ratio of 

Equivalent weight of an element is the mass of element that combines with one equivalent of Oxygen i.e., with 8g of Oxygen.

In CO, 12g Carbon combined with 16g of Oxygen or 6g Carbon combines with 8g Oxygen. So, equivalent weight of Carbon in CO is 6.

In ${\mathrm{CO}}_2$, 12g Carbon combined with 32g of Oxygen or 3g Carbon combines with 8g of Oxygen. So, equivalent weight of Carbon in ${\mathrm{CO}}_2$ is 3.

Ratio of equivalent weights of Carbon in CO and ${\mathrm{CO}}_2$ is 6:3 or 2:1