With the decrease in prices of tea by 15 % Tonu, the chaiwallah, … - Vidyadip

Question

With the decrease in prices of tea by $15\%$ Tonu, the chaiwallah, was able to buy $2\ kg$ more of tea with the same $Rs. 45$ that he spent each month on buying tea leaves for his chai shop. What was the reduced price of tea? What was the original price of tea?

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Answer

Let chaiwallah purchase $y$ kg tea.
Let price of tea per kg $= Rs. x$
Discount $15\%$ per kg$=\text{x}-\frac{15}{100}\times\text{x}=\frac{85\text{x}}{100}$
Chailwallah can buy $2\ kg$ extra with $15\%$ discount.
But without discount,$xy = 45$
$\Big(\text{x}-\frac{15}{100}\Big)\times\text{x}=\Big(\frac{85\text{x}}{100}\Big)(\text{x+2})=45$
After solving Eqs. $(i)$ and $(ii)$
$\frac{85}{100}(45)+\frac{85\times2\text{x}}{100}=45$
$\text{45}\Big[1-\frac{85}{100}\Big]=\frac{85\times2\text{x}}{100}$
$\frac{45\times15}{100}=\frac{85\times2\text{x}}{100}$
$\text{x}=\frac{45\times15}{2\times85}=\frac{135}{34} \ \text{per} \ \text{kg}$$=3.97 \ \text{per} \ \text{kg}$
Reduced price$=\frac{85}{100}\times3.97=\frac{337.45}{100}$$=3.3748=3.38 \ \text{per} \ \text{kg}$

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