Answer:
Given: Initial Total Expenditure (\[T{{E}_{0}}\]) = Rs. 60 Final Total Expenditure (\[T{{E}_{1}}\]) = Rs. 60 Initial Price (\[{{P}_{0}}\]) = Rs. 5 Percentage change in price = \[-Rs.\text{ }20\] Percentage change in price =\[\frac{{{P}_{1}}-{{P}_{0}}}{5}\times 100\] \[-20=\frac{{{P}_{1}}-5}{5}\,\,\times \,\,100\] \[\frac{-100}{100}={{P}_{1}}-5\] \[{{P}_{1}}\] = 4 Price (P) Total Expenditure (TE) = Price (P) \[\times \] Quantity (Q) Quantity Q=\[\frac{TE}{P}\] \[{{P}_{0}}=Rs\,\,5\] \[T{{E}_{0}}=\,\,Rs\,\,60\] \[{{Q}_{0}}=\,\,12\] \[{{P}_{1}}=Rs\,\,4\] \[T{{E}_{1}}=\,\,Rs\,\,60\] \[{{Q}_{1}}=\,\,15\] Now, \[{{E}_{d}}=(-)\frac{\text{Percentage}\,\,\text{change}\,\,\text{in}\,\,\text{quantity}\,\,\text{demanded}}{\text{Percentage}\,\,\text{change}\,\,\text{in}\,\,\text{price}}\] \[{{E}_{d}}=(-)\frac{\,\frac{{{Q}_{1}}-{{Q}_{0}}}{{{Q}_{0}}}\,\,\times \,\,100}{-20}\,\,\] \[{{E}_{d}}=(-)\frac{\,\frac{15-12}{12}\,\,\times \,\,100}{-20}\,\,\] \[{{E}_{d}}=(-)\frac{25}{-20}\] \[{{E}_{d}}\]= 1.25 \[\therefore \] \[\] Thus, the price elasticity of demand is 1.25.
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