Si los 2 / 5 de 1 / 3 del producto de dos números que son entre sí como 4 es a 5, es 384, ¿Cuál es la suma de las cifras del mayor de tales números?

<img src="https://tex.z-dn.net/?f=%20%5Ccdot%5C%20%5Ctext%7BPrimero%20vamos%20a%20averiguar%20cu%5C%27ales%20son%20los%20n%5C%27umeros%2C%20y%20para%20ello%20utilizaremos%7D%5C%5C%5Ctext%7Buna%20constante%20de%20proporcionalidad%7D%5C%20%5Cboldsymbol%7B%28k%29%7D%2C%5Ctext%7Bentonces%3A%7D%5C%5C%20%5C%5C%5Ctextbf%7BSEA%3A%7D%5C%5C%5Cboldsymbol%7B4k%3A%7D%5Ctext%7BEl%20n%5C%27umero%20menor.%7D%5C%5C%5Cboldsymbol%7B5k%3A%7D%5Ctext%7BEl%20n%5C%27umero%20mayor.%7D%5C%5C%20%5C%5C%5Ctextbf%7BRESOLVIENDO%3A%7D%5C%5C%5Ccdot%5Ctext%7BSi%20nos%20indican%20que%20los%7D%5C%20%5Cboldsymbol%7B%5Cfrac%7B2%7D%7B5%7D%7D%5C%20%5Ctext%7Bde%7D%5C%20%5Cboldsymbol%7B%5Cfrac%7B1%7D%7B3%7D%7D%5C%20%5Ctext%7Bdel%20producto%20de%20dos%20n%5C%27umeros%20es%20igual%20a%7D%5C%20%5Cboldsymbol%7B384%7D%2C%5C%5C%5Ctext%7Bentonces%20debemos%20multiplicar%3A%7D%20" /><img src="https://tex.z-dn.net/?f=%20%5Cleft%28%5Cdfrac%7B2%7D%7B5%7D%5Cright%29%5Ccdot%5Cleft%28%5Cdfrac%7B1%7D%7B3%7D%5Cright%29%5Ccdot%284k%29%5Ccdot%285k%29%3D384%5C%5C%20%5C%5C%20%5C%5C%5Cleft%28%5Cdfrac%7B2%7D%7B15%7D%5Cright%29%5Ccdot%2820k%5E2%29%3D384%5C%5C%20%5C%5C%20%5C%5C%5Cdfrac%7B2%2820k%5E2%29%7D%7B15%7D%3D384%5C%5C%20%5C%5C40k%5E2%3D15%28384%29%5C%5C%20%5C%5C40k%5E2%3D5760%5C%5C%20%5C%5Ck%5E2%3D%5Cdfrac%7B5760%7D%7B40%7D%5C%5C%20%5C%5Ck%5E2%3D144%5C%5C%20%5C%5Ck%3D%5Csqrt%7B144%7D%5C%5C%20%5C%5Ck%3D12%5Cquad%5CLongrightarrow%5Ctext%7BLa%20constante%20de%20proporcionalidad.%7D%20" />

<img src="https://tex.z-dn.net/?f=%20%5Ctextbf%7BAhora%20despejamos%3A%7D%5C%5C%20%5C%5C%5Cboldsymbol%7B4k%5Cto%7D4%2812%29%3D48%5Cquad%5CLongrightarrow%5Cboxed%7B%5Ctext%7BEl%20n%5C%27umero%20menor.%7D%5C%20%5Ccheckmark%7D%5C%5C%20%5C%5C%5Cboldsymbol%7B5k%5Cto%7D5%2812%29%3D60%5Cquad%5CLongrightarrow%5Cboxed%7B%5Ctext%7BEl%20n%5C%27umero%20mayor.%7D%5C%20%5Ccheckmark%7D%5C%5C%20%5C%5C%20%5C%5C%5Ccdot%5Ctext%7BEl%20n%5C%27umero%20mayor%20es%7D%5C%20%5Cboldsymbol%7B60%7D%2C%5C%20%5Ctext%7Bpero%20nos%20piden%20hallar%20la%20suma%20de%20sus%20cifras%2C%7D%5C%5C%5Ctext%7Bentonces%3A%7D%5C%5C%20%5C%5C6%2B0%3D6%5Cquad%5CLongrightarrow%5Cboxed%7B%5Cboxed%7B%5Cmathbb%7BRESPUESTA%7D%7D%7D%20" /><img src="https://tex.z-dn.net/?f=%20%5Ctextbf%7BMUCHA%20SUERTE...%21%21%7D%20" />.