This would almost instantly produce systemic disenfranchisement of racial and cultural minorities, and in the long run, destroy social cohesion within the nation. The reason is, the majority group would automatically (if not intentionally) write the test in a way that make sense only for that cultural group, and since the test is a literacy test (i.e. based on language arts skills), this effect is especially pronounced.
A real world example of this is the controversy surrounding culturally biased questions on the SAT that advantage students who are native speakers of the majority “white” dialect of English. It is a simple fact of life that there will be differences in culture between different groups of humans, and that some concepts and expressions that make sense in one culture may not translate as well or come as easily to a native of another culture.
Such a system may work just fine in a relatively homogenous country with little diversity. However, in a multicultural society, this would be an invitation for complaints of “bias!!!”, founded or unfounded. Leaders of large minority groups in such a country may discover that it is possible to reflexively claim “the test is biased!”, since members who fail the test will naturally blame the test, whether or not it’s really biased. We see this commonly in the United States today, which does not even use literacy tests for something as important as voting. Leaders like these may play on fears of racism or discrimination to consolidate their influence, producing subnations and tribal loyalties within the country and a “trust no other color” attitude among members of the minority groups. The end result would be one of three possibilities:
Discrimination is expanded and made explicit
The majority group internalizes the complaints of bias and racism in the tests, and simply decides that biased tests are a fact of life and moves to make the tests even more biased towards the majority. Essentially “if we are accused of being racists, we might as well get something out of it”. The result is something of an apartheid society.
The nation breaks apart
Minority groups decide they want no part in a discriminatory system, and divide the country. If they are scattered across the country, they may reach an agreement with the majority to form reservations or enclaves which would be nominally self governing. If they are concentrated in one geographic area, they may simply secede. This scenario has the highest likelihood of violence and bloodshed, as partitioning a nation is usually a very messy and blood-drenched process.
They get rid of the test.
Supporters of democracy on both sides may foresee the consequences of such a system, and decide that a national literacy test is simply not worth the social strife, and move to eliminate it and reinstate universal adult suffrage.