How many sons does Mister Johnson have in the following case? Mister Johnson leaves a idol of height 24 cm in his will to his sons. The gold that the idol is made of is equally divided by creating similar idols of height 12 cm for each son. How many sons are there?

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Mister Johnson leaves behind an idol which has a height of 24 cm. This is to be used to create smaller idols with a height of 12 cm and one given to each of his sons.

The volume of the original idol is proportional to the cube of the height. Let the factor that equates height and volume be K.

V = K*(24)^3

Now the idol is used to create idols that are 12 cm tall. The factor of proportionality K remains the same. If the volume of each statue if V'

V' = K*(12)^3

V/V' = K*24^3 / K*12^3

=> (24/12)^3

=> 2^3

=> 8

This gives the number of sons = 8.

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