Question

The amount of extension in an elastic string varies directly as the weight hung on it. If a weight of 150 gm produces an extension of 2.9 cm, then what weight would produce an extension of 17.4 cm?

Answer 1

Let x gm be the weight that would produce an extension of 17.4 cm.
 

Weight (in gm)	150	x
Length (in cm)	2.9	17.4

\[ \text{ Since the amount of extension in an elastic string and the weight hung on it are in direct variation, we have } : \]
\[\frac{150}{x} = \frac{2 . 9}{17 . 4}\]
\[ \Rightarrow 17 . 4 \times 150 = 2 . 9 \times x\]
\[ \Rightarrow x = \frac{17 . 4 \times 150}{2 . 9}\]
\[ = \frac{2610}{2 . 9}\]
\[ = 900\]
\[\text{ Thus, the required weight will be 900 gm }  .\]