A reduction of 10% in the price of tea enables a dealer to purchase 25 kg more tea for Rs. 22500. What is the reduced price per kg of tea?

Solution(By Examveda Team)

$$\eqalign{ & {1^{st}}\,{\text{Method}}: \cr & {\text{Let}}\,{\text{the}}\,{\text{original}}\,{\text{prine}}\,{\text{of}}\,{\text{tea}}\,{\text{be}}\,{\text{Rs}}.\,x\,\text{kg} \cr & {\text{After reduction the price becomes}} \cr & = x - 10\% \,\text{of}\,x = \frac{{9x}}{{10}}\,\text{per kg} \cr & {\text{Now}}, \cr & {\frac{{22500}}{{ {\frac{{9x}}{{10}}} }}} - \frac{{22500}}{x} = 25 \cr & {\text{or}},\,22500\left[ {\frac{{10}}{{9x}} - \frac{1}{x}} \right] = 25 \cr & {\text{or}},\,25 \times 9x = 22500 \cr & {\text{or}},\,x = {\frac{{22500}}{{25\times9}}} = \text{Rs.}\,100 \cr & {\text{Hence,}}\,{\text{new}}\,{\text{price}} \cr & = 90\,{\text{per}}\,{\text{kg}}{\text{}} \cr }$$

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$$\eqalign{ & {\text{Thought}}\,{\text{process}}\,{\text{method:}} \cr & {\text{Let the original price be Rs}}{\text{. 100 per kg}}, \cr & {\text{He get tea}} = \frac{{22500}}{{100}} \cr & = 225\,\text{kg} \cr & {\text{After reduction the price becomes}} \cr & = {\text{ }}90{\text{ per kg}} \cr & {\text{He}}\,{\text{get}}\,{\text{tea}} = \frac{{22500}}{{90}} \cr & = 250\,\text{kg} \cr & {\text{So, reduction price is }}{\text{ Rs. }}90{\text{ per kg}} \cr & {\text{As it enables him to buy 25 kg of more tea}}{\text{.}} \cr} $$