Three numbers are in the ratio 1 : 2 : 3 and the sum of their cubes is 4500. Find the numbers.
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Let the three numbers be x, 2x and 3x.
According to the question, (x)3+(2x)3+(3x)3=4500⇒x3+8x3+27x3=4500⇒36x3=4500⇒x3=450036 ⇒x3=125 [taking cube root on both sides] ⇒x=3√125⇒x=3√5×5×5∴x=5
Hence, the numbers are 5, 2×5 and 3×5 i.e. 5, 10 and 15.