NEW DELHI—India’s biggest economic asset is fast turning into its most daunting challenge: hundreds of millions of young people.

Two-thirds of India’s 1.2 billion people are below 35 years of age. That’s more than two times the total U.S. population. Unlike Japan, China and Europe, whose working-age populations have peaked, India’s is growing and is estimated to become the world’s largest. But the world’s second-most-populous country is struggling to tap this demographic dividend.

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