Answer:
Smallest Number = 35
Other Number = 42
Step-by-step explanation:
Let the smaller number be x.
Let the other number be y.
Given:
x : y = 5 : 6
That is,
[tex]\frac{x}{y} = \frac{5}{6}[/tex]
[tex]=> 5y = 6x\\\\=>x = \frac{5y}{6}[/tex]
Next: Let the smaller number be reduced by 5, x - 5
Let the other number be increased by 3, y + 3
Given : (x - 5) : (y + 3) = 2 : 3
That is,
[tex]\frac{x-5}{y+3} = \frac{2}{3}\\[/tex]
[tex](x-5) \times 3 = (y+3)\times 2\\\\substitute \ x = \frac{5y}{6}\\\\3(\frac{5y}{6} -5) = 2y + 6\\\\\frac{5y}{2} - 15 = 2y + 6\\\\\frac{5y}{2} - 2y = 6 + 15\\\\\frac{5y-4y}{2} = 21\\\\y = 21 \times 2 = 42\\\\Substitute \ y \ in \ x = \frac{5y}{6} \\\\x = \frac{5 \times 42}{6} = 35[/tex]
