Why is India providing aid to other nations when 30% of its population lives in abject poverty?

Parable of the book

Raju was a kid whose family lived in abject poverty. He didn't have good clothes or food. However, he was able to save a few paise that he earned from a variety of sources. One day, he was able to save up to 10 rupees. He happily went to the shop and bought a book. A puzzled bystander asked him, "should you not be buying better clothes or food with this money, instead of buying a book?"

Raju replied: "I'm buying the book now so that someday I would neither have to worry about my tattered clothes nor have to bother about answering such questions."

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A lot of us have a very poor understanding of what it means to solve poverty. Poverty is not as simple as pouring money into a pit.  As long as the bucket is leaky it doesn't matter how many gallons of water you pour into it. A wise man would first fix the bucket. Poverty is a complicated social phenomenon caused by a variety of factors and wise government would fix them.

Why does India provide aid:

1. Aid strengthens economy: India provides aid to Afghanistan and other friends across the developing world. This is because Afghanistan and these friends also trade a lot with India. Trade is the best antidote to poverty. When our friends are strong, India's interests will be strong even if they don't repay the debts in any way. When India is strong, we will have more tools to solve poverty.
2. Aid reduces migrations: India provides a lot of aid to countries like Sri Lanka that previously had refugee flows into India. By stabilizing Sri Lanka, India can save money spent on managing refugees.
3. Aid pushes out other interests: Sri Lanka was looking to move to China's sphere and that was dangerous to India. This would have increased India's defense expenses and also impacted trade with Sri Lanka [as China can be a bigger partner than them]. However, the aid helped them win back to Indian sphere of interest. In short, that is an investment. 
4. Who we want to be? Even the poorest people help their neighbors out in times of crisis. And it is usually reciprocal. India would provide aid to Nepal when it is trouble and Nepal would do the same when India is in trouble.

India's foreign aid policy is well thought out and strategic. India benefits much more from this intangibly. When India benefits its poor benefit too. Or in other words foreign aid indirectly solves domestic poverty.