Question

Onion is sold for 5 consecutive months at the rate of Rs 10, 20, 25, 25, and 50 per kg, respectively. A family spends a fixed amount of money on onion for each of the first three months, and then spends half that amount on onion for each of the next two months. The average expense for onion, in rupees per kg, for the family over these 5 months is closest to

Accepted Answer

A. Let the family spend Rs $2x$ in each of the first three months, and Rs $x$ in each of the next two months. Total expense $= 2x + 2x + 2x + x + x = 8x$. Quantity bought in each month: - Month 1: $\frac{2x}{10} = 0.20x$ - Month 2: $\frac{2x}{20} = 0.10x$ - Month 3: $\frac{2x}{25} = 0.08x$ - Month 4: $\frac{x}{25} = 0.04x$ - Month 5: $\frac{x}{50} = 0.02x$ Total quantity bought $= (0.20 + 0.10 + 0.08 + 0.04 + 0.02)x = 0.44x$. Average price per kg $= \frac{	ext{Total Expense}}{	ext{Total Quantity}} = \frac{8x}{0.44x} = \frac{800}{44} = \frac{200}{11} \approx 18.18	ext{ Rs/kg}$. Closest integer is $18$.

Average Onion Price per kg

Explanation

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