The ratio of two numbers is 2:3 and the sum of their cubes is 945. The difference of number is?

A). 1

B). 2

C). 3

D). 4

3

2x 

Solution:

Let the two numbers be \'x\' and \'y\'.

Given:-

x : y = 2 : 3 -------->1  and 

x³ + y³ = 945 --------> 2

From 1st equation we get, x = ⅔ y . Substituting this in the 2nd equation we get, 

(⅔)³ y³ + y³ = 945

(8y³/27) + y³ = 945

y³(1 + 8/27) = 945

y³(35/27) = 945

y³ = 945 × (27/35)

y³ = 27 × 27

y³ = 3³ × 3³

y = (3³ × 3³)⅓

y = 3 × 3

y = 9

So, x = ⅔(9)

x = 6

So, the difference between the two numbers is (9-6) which is 3 .

The correct option is C). 3

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