1.

Find two numbers such that their mean proportional is 18 and the third proportional to them is 144.1). 6 and 422). 9 and 363). 3 and 184). 6 and 12

Answer»

Let the NUMBERS are x and y,

Mean proportional = √xy = 18

⇒ xy = 324---- (1)

THIRD proportional = y2/x = 144

⇒ y2 = 144x---- (2)

Putting the value of x from this in 1st equation,

⇒ y3/144 = 324

⇒ y3 = 324 × 144

⇒ y3 = 18 × 18 × 18 × 8

⇒ y = 18 × 2

⇒ y = 36 and x = 324/36 = 9

∴ Two numbers are 9 and 36.


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