Official Explanation

RO1

Notice that in the equation provided, the ratio of the height of the lamppost to the height of the boy \([\frac{8}{1.6}]\) is equal to the ratio of the boy's distance from the lamppost plus the length of the shadow to the length of the shadow alone \([\frac{6+1.5}{1.5}]\). Thus, since the distance from the lamppost is 8, substituting x for the length of the shadow into the equation yields \(\frac{8}{1.6}=\frac{8+x}{x}\). Cross-multiplying, \(8x = 1.6(8 + x) = 12.8 + 1.6x.\) Subtracting 1.6x from each side of the equation gives \(6.4x = 12.8.\) Dividing both sides by 6.4 yields x = 2.

The correct answer is 2.

RO2

Using the equation described in the analysis of RO1, substitute 3 for the length of the shadow and y for the distance from the lamppost. Thus, \(\frac{8}{1.6}=\frac{y+3}{3}\). Cross-multiplying, \(24 = 1.6(y + 3) = 1.6y + 4.8.\) Subtracting 4.8 from each side of the equation, 19.2 = 1.6y. Dividing each side by 1.6, 12 = y.

Alternatively, one could observe that in the diagram, the ratio of the distance from the lamppost to the length of the shadow is \(\frac{6}{1.5}\). Since we are told the length of the shadow is 3 m, which is twice the length in the diagram, one could simply double the distance from the lamppost in the diagram to get a distance of 12 m.

The correct answer is 12.