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Question: If 20 is divided into two parts such that product of one part and the cube of other is maximum, then...

If 20 is divided into two parts such that product of one part and the cube of other is maximum, then ratio of the two parts is –

A

1 : 1

B

2 : 3

C

1 : 3

D

) 1 : 4

Answer

1 : 3

Explanation

Solution

Let one part be x then other will be 20 – x

y = x (20 – x)3

= (20 – x)3 + 3x (20 – x)2 (–1)

= (20 – x)2 (20 – 4x)

= 0

Ž x = 5

other part is

= = 515\frac { 5 } { 15 } = 1/3