Crunching the Numbers: Analyzing the Average Expense of Onion for a Family over 5 Months

Firstly, we need to establish how many kilograms of onions were bought each month. In the first month, the family spent a certain fixed amount at a rate of Rs 10 per kg, which means they bought the fixed amount divided by 10 in kg. Let's assume the fixed amount spent by the family is 'A'. Therefore, the quantity of onions bought in the first month would be A/10 kg. In the second month, they spent the same fixed amount at a rate of Rs 20 per kg, which means they bought A/20 kg. In the third month, they bought A/25 kg given that the rate is Rs 25 per kg. For the next two months, they spent half the fixed amount at rates of Rs 25 per kg and Rs 50 per kg, respectively. Therefore, they bought (A/2)/25 = A/50 kg in the fourth month, and (A/2)/50 = A/100 kg in the fifth month. The total quantity of onions bought over the five months would be the sum of monthly quantities i.e., A/10 kg + A/20 kg + A/25 kg + A/50 kg + A/100 kg. Now, let's calculate the total expense spent by the family over these five months. The total spend is 3A (for the first three months) plus A (which is half of the fixed amount, spent over the last two months), which is 4A in total. The average expense per kg would be the total money spent divided by the total quantity of onions bought. When we divide the total cost (4A) by the total quantity of onions, the A's cancel out, and we end up with: 4A / (A/10 + A/20 + A/25 + A/50 + A/100) = 4 / (1/10 + 1/20 + 1/25 + 1/50 + 1/100) = 4 / (0.1 + 0.05 + 0.04 + 0.02 + 0.01) = 4 / 0.22 = approximately 18.18 So, the average expense for onions, per kg, for the family over these 5 months is closest to Rs 18.18.