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Average Onion Price per kg

CAT 2021 Slot 2 · Quantitative Ability · Medium · Averages

This is a medium Quantitative Ability question from the CAT 2021 Slot 2 paper. It tests Averages. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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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

  1. A.

    18

  2. B.

    26

  3. C.

    16

  4. D.

    20

Answer

A

Explanation

Let the family spend Rs 2x2x in each of the first three months, and Rs xx in each of the next two months.

Total expense =2x+2x+2x+x+x=8x= 2x + 2x + 2x + x + x = 8x.

Quantity bought in each month:

  • Month 1: 2x10=0.20x\frac{2x}{10} = 0.20x
  • Month 2: 2x20=0.10x\frac{2x}{20} = 0.10x
  • Month 3: 2x25=0.08x\frac{2x}{25} = 0.08x
  • Month 4: x25=0.04x\frac{x}{25} = 0.04x
  • Month 5: x50=0.02x\frac{x}{50} = 0.02x

Total quantity bought =(0.20+0.10+0.08+0.04+0.02)x=0.44x= (0.20 + 0.10 + 0.08 + 0.04 + 0.02)x = 0.44x.

Average price per kg =Total ExpenseTotal Quantity=8x0.44x=80044=20011≈18.18 Rs/kg= \frac{\text{Total Expense}}{\text{Total Quantity}} = \frac{8x}{0.44x} = \frac{800}{44} = \frac{200}{11} \approx 18.18\text{ Rs/kg}. Closest integer is 1818.

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