This is the Important question based on Arithmetic progression Chapter of R.S Aggarwal book for ICSE & CBSE Board.
Here you have to Find the numbers by divide 24 in three parts which will make an AP with the help of their Given Product.
Question Number 5 of Exercise 11 B of RS Aggarwal Solution
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Divide 24 in three parts such that they are in AP and their product is 440.
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Let a – d, a, a + d are three numbers in AP.
their sum = a – d + a + a + d = 24
3a = 24
or a = 8
Again,
Their Product = (a – d) x a x (a + d) = 440
a(a² – d²) = 440
8(8² – d²) = 440
or d = ±3
Numbers are : (5, 8, 11) or (11, 8, 5)