Onion is sold for 5 consecutive months at the rate of Rupees 10, 20

Question

Onion is sold for 5 consecutive months at the rate of Rupees 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:

A. 26
B. 21
C. 20
D. 18
E. 16

A. 26
B. 21
C. 20
D. 18
E. 16

yashikaaggarwal · Answer

I couldn't comprehend the "that" in the following statement: then spends half  that  amount on onion for each of the next two months.

Is it half the amount spent on each initial 3 months or
Half the amount spent on all 3 months combined.
Either way. I am getting the maximum average of 8 (10+10+10+5+5 = 40/5 = 8) and 12 (10+10+10+15+15 = 60/5 = 12)
Which is closer to E aka 16.

Where am I getting wrong?

Posted from my mobile device

kapilsingal27 · Answer

Let's consider in first three months money spend = rs 100 each
In forth and fivth month money spend= rs 50 each
So, in first month onion purchased =100 rs/ 10 rs per kg = 10 kg
In second = 100 rs/ 20 rs per kg = 5 kg 
In third = 100rs /25 rs per kg= 4 kg
In forth= 50/25= 2kg
In fivth = 50/50=1 kg

Total onion= 22 kg
Total money spend= 400
Average expanse= total money/total onion =400/22= 18.18 
Ans is D

Posted from my mobile device

yashikaaggarwal · Answer

So the quantity purchased could be anything?

sujoykrdatta · Answer

The prices per kg are 10, 20, 25, 25, and 50
Thus, for ease of calculations, we assume the money spent each month (for the first 3 months) = Rupees 100

Thus, the quantities purchased for the first 3 months are: 
First month: 100/10 = 10 kg
Second month: 100/20 = 5 kg
Third month: 100/25 = 4 kg

Money spent each month (for the next 2 months) = Rupees 100/2 = Rupees 50
Thus, the quantities purchased for the last 2 months are: 
Fourth month: 50/25 = 2 kg
Fifth month: 50/50 = 1 kg

Total money spent = 100 x 3 + 50 x 2 = Rupees 400
Total quantity = 10 + 5 + 4 + 2 + 1 = 22 kg
Thus, average expense for onion, in Rupees per kg = 400/22 = 200/11 = 18.18

Answer D

The video solution is given below (subscribe to the channel below):

https://www.youtube.com/watch?v=dv_if3LsxP8

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Onion is sold for 5 consecutive months at the rate of Rupees 10, 20

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Onion is sold for 5 consecutive months at the rate of Rupees 10, 20

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