In a correct clock:
After 60 min , angle b/w min hand and hour hand is 300.
min hand makes 60 in 1 min. and hour hand makes ½0 in 1 min.
let they meet after t min.
min hand will make a degree t×6 and hour hand will make a degree t×½
So, t×6 = t×½ + 300 (already made 300)
solve: t=60/11 min.
total time taken for overtaking 60 + 60/11 = 720/11 min. = 65 and 5/11 min.
So, In the faulty close the hand meet after 65 min.
In 65 min we get 5/11 min extra
In 1 ------------------5/(11×65) min.
in 60 min ---------------- (5×60)/(11×65)min
in 24 hour ---------------- (24× 5× 60 ) / (11×65) min
=$\frac{5\times 60\times 24}{11\times 65} = \frac{1440}{143} min$