Discussion

Explanation:

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Growth rate in production = $\left(\frac{\mathrm{Difference} \mathrm{in} \mathrm{production} \mathrm{in} 2011 \mathrm{and} 2005}{\mathrm{Production} \mathrm{in} 2005}\right)$ × 100

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From the table given in the solution to the first question of the set:

Production of Aluminium in 2006 = 75 million tonnes.

Production of Aluminium in 2011 = 105 million tonnes

∴ Growth rate = $\left(\frac{30}{75}\right)$ × 100 = 40%

Average growth rate = $\frac{40}{5}$ = 8%

If this rate continues, the production of aluminium in 2015 will be

105 + $\frac{105\times 4\times 8}{100}$ = 138.6 million tonnes

The closest option is 140 million tonnes.

Hence, option (b).

Note:

The question does not specify whether simple or compounded average growth is to be considered. If we consider a compounded growth, the annual rate of growth would be

$\left({\left(\frac{105}{75}\right)}^{\frac{1}{5}}-1\right)$ × 100 = 106, which is 6%

The production in 2015 would then be 105 × (1.06)⁴ = 132.56, which is not available in the options.

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