I think you cannot totally blame the Indian government as their fault or give credit to China government on this agenda of education. Though China government, being CPC controlled, can enforce education program in a more efficient way without caring about votes of other interested factions like the taxed rich, education is a deep-rooted East Asian philosophy. In East Asia, individuals, families, can sacrifice other things for education. If you look at PISA scores you might find this pattern:
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65 countries (34 OECD, 31 Partnering), 2012 results
Programme for International Student Assessment - Wikipedia, the free encyclopedia
So I don't think India government should use China as a benchmark for education, however more input does seem necessary for the benefits of all its people.
In it's relation to defense budget, some reference for you. Notice that China launched compulsory education in 1986? It was the year immediately after the retrenchment of PLA was completed in 1985. The retrenchment started back in 1980, the year immediately after diplomatic relationship was formalized between China and the biggest threat - USA - in 1979, easing the security environment of China. Deng Xiaoping set the order diplomacy -> defense cut -> boost education.