$$\frac{1}{9}$$ of X = $$\frac{1}{10}$$ of Y, so X : Y = 9 : 10. Y is greater than X by 100.<br><br>[[model:questions/solutions/q4363.png]]<br><br>• $$\frac{1}{9}$$ X = $$\frac{1}{10}$$ Y ⇒ $$\frac{X}{9}$$ = $$\frac{Y}{10}$$ ⇒ 10X = 9Y ⇒ X : Y = 9 : 10<br>• Y − X → 10u − 9u = 1u → 100<br>• X = 9 × 100 = 900, Y = 10 × 100 = 1000<br>• Sum → X + Y = 900 + 1000 = 1900<br><br>The sum of X and Y is 1900.<br>Check: $$\frac{1}{9}$$ × 900 = 100. $$\frac{1}{10}$$ × 1000 = 100. Equal. ✓