What has Hands But cannot Clap is a Clock or a Watch.
A Clock technically has 3 hands.
1 Hour Hand Which tells Hours
1 Minute Hand Which tells Minutes
1 Second Hand Which tells Seconds.
But cannot clap with these hands.
Since they can do 19 programs in 19 hours, Then 52 programs in 52 hours respectively.
And a 15 min interval
Total time they take to do 52 programs is 52 hours 15 minutes.
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