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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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Solution
Given, chaiwala can buy 2 kg extra with 15% discount.
⇒ Let us assume chaiwala purchase y kg tea.
And price of a tea per kg = Rs. x
⇒ Discount 15% per kg = `x - 15/100 xx x`
= `(100x - 15x)/100`
= `(85x)/100`
The amount spent by him for purchasing tea leaves is 45
Without discount he can buy xy = 45 ...[Equation 1]
And `((85x)/100) (y + 2) = 45` ...[Equation 2]
Solving above two equations we get,
`(85xy + (85 xx 2x))/100`
⇒ `(85(45))/100 + (85 xx 2x)/100 = 45`
⇒ `(85 xx 2x)/100 = 45 - (85(45))/100`
⇒ `(85 xx 2x)/100 = 45[1 - 85/100]`
⇒ `(85 xx 2x)/100 = (45 xx 15)/100`
⇒ 85 × 2x = 45 × 15
⇒ `x = (45 xx 15)/(2 xx 85)`
⇒ `x = 675/170`
⇒ x = 3.97 per kg
Hence, original price = 3.97 per kg
∴ Price reduced = `85/100 xx 3.97` = 3.374
Approximately 3.38 per kg
Hence, Reduced price is 3.38 per kg.
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