Question 1041255
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two numbers are in ratio 4:5. if difference of their cubes is 61, find the number
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<pre>
{{{x/y}}} = {{{4/5}}} --->

{{{x^3/y^3}}} = {{{4^3/5^3}}} = {{{64/125}}}.


Let a = {{{x^3}}}, b = {{{y^3}}}.

Then 

{{{a/b}}} = {{{64/125}}}     (1)   and
b - a = 61.       (2)

---> a = {{{(64/125)*b}}}  --->  b - {{{64/125}}} = 61  --->  125b - 64b = 61*125  --->  61b = 61*125  --->  b = 125  --->  {{{y^3}}} = 125  --->  y = {{{root(3,125)}}} = 5.

Then x = 4.
</pre>

Solved.