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CAT 2021 Slot 1 — QA Question 13

Weighted AverageEasy

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

Answer & solution

  • A

    20

  • B

    16

  • 18

  • D

    26

Solution

Easy

"Average expense per kg" is total money spent divided by total kilograms bought — not the average of the rates. Fix a convenient money figure per month, compute kilograms bought each month, then divide totals.

1

Choose a convenient spend. Let the family spend Rs 100\text{Rs }100 in each of the first three months (a multiple of all the rates), so they spend half, Rs 50\text{Rs }50, in each of the next two months.

2

Kilograms bought each month =spendrate=\dfrac{\text{spend}}{\text{rate}}.

Month 1: 100/10=10 kgMonth 2: 100/20=5 kgMonth 3: 100/25=4 kgMonth 4: 50/25=2 kgMonth 5: 50/50=1 kg\begin{aligned} &\text{Month 1: }100/10=10\ \text{kg}\\ &\text{Month 2: }100/20=5\ \text{kg}\\ &\text{Month 3: }100/25=4\ \text{kg}\\ &\text{Month 4: }50/25=2\ \text{kg}\\ &\text{Month 5: }50/50=1\ \text{kg} \end{aligned}
3

Totals.

Total kg=10+5+4+2+1=22Total spend=100+100+100+50+50=400\begin{aligned} &\text{Total kg}=10+5+4+2+1=22\\ &\text{Total spend}=100+100+100+50+50=400 \end{aligned}
4

Average expense per kg.

40022=18.18…≈18(per kg)\begin{aligned} &\frac{400}{22}=18.18\ldots\approx 18\quad\text{(per kg)} \end{aligned}
Rs 18 per kg (option c)\text{Rs }18\text{ per kg (option c)}

Common trap: averaging the rates gives 10+20+25+25+505=26\tfrac{10+20+25+25+50}{5}=26, which ignores how much was actually bought at each price.

CAT 2021 Slot 1 QA Q13: Onion is sold for 5 consecutive months at the rate of Rs 10, 20, 25, 25, and 50 per kg, respectively. A family — Solution | TheCATExam