Needy = very poor, being in need, lacking the necessities of life.

• There are many needy people in our village.
• The government should earmark funds to extend humanitarian assistance to the needy.
• During the worst flood Kerala has ever witnessed  the youngsters went around and collected food and clothes for the needy.
• The banks should come forward to assist the needy families with interest-free loans for the education of their children.

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Needful = what is necessary, requisite.

• You may forward the application before it is too late, and we will do the needful.
• The flood situation is very grave and so the matter should be dealt with the needful urgency and attention.
• It is the duty of the police to do the needful when there is a break-out of violence.