1.

The product of two consecutive natural numbers which are multiples of 3 is equal to 810. Find the two numbers.

Answer»

Let the two consecutive natural numbers which are multiples of 3 be 3x and 3(x + 1). 

Now, 3x(3x + 3) = 810 

⇒ x2 + x = 90 

⇒ x2 + x – 90 = 0 

⇒ (x + 10) (x – 9) = 0 

⇒ x = 9 or x = – 10 

Rejecting negative value of x, because numbers are natural. We have x = 9. 

Hence, the required numbers are 27 and 30.



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