Problematics | The price of mixing apples and oranges - Hindustan Times
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Problematics | The price of mixing apples and oranges

Feb 28, 2023 08:45 AM IST

It may be fine to compare apples with oranges, but you should be wary about mixing the two, except perhaps in a fruit salad. Here’s why.

The idea that you cannot compare apples with oranges could well be a notion. In 1995, the Annals of Improbable Research, a magazine best known for handing out the Ig Nobel prizes, published a study by NASA physicist Scott Sandford noting several similarities between the two fruits.

Welcome to Problematics! (Shutterstock) PREMIUM
Welcome to Problematics! (Shutterstock)

Five years later, a somewhat similar study appeared in the British Medical Journal. This one compared six apples and six oranges, which became five and six after “the author's 12-year-old son, Thomas, inadvertently consumed one of the objects, an apple”. The study recorded similarities in size and sweetness, and noted differences only in the categories of colour and seeds.

“The admonition ‘Let's not compare apples with oranges’ should be replaced immediately with a more appropriate expression such as ‘Let's not compare walnuts with elephants’ or ‘Let's not compare tumour necrosis factor with linguini’,” noted the author, James E Barone, an American surgeon.

Be warned, though. It may be fine to compare apples with oranges, but you should be wary about mixing the two, except perhaps in a fruit salad. Here’s why.

#Puzzle 27.1.
#Puzzle 27.1.

We have two couples who sell apples and oranges. One couple offers reasonable rates: Mr A’s apples @ 350 for 3 kg and Ms A’s oranges @ 175 for 2 kg. The other couple’s rates are even lower: Mr B’s apples @ 175 for 2 kg and Ms B’s oranges @ 175 for 3 kg.

One day, Couple A offers a package deal that attempts to combine the individual prices for 3 kg apples and 2 kg oranges, i.e. 350 + 175 = 525 for 5 kg mixed fruit.

Not to be outdone, Couple B offers a similar deal for a 5 kg mixed package @ 175 + 175 = 350.

Let’s look at their earnings. Mr and Mrs A pool their 30 kg apples and 30 kg oranges. At original prices, these would have fetched them 3,500 + 2,625 = 6,125. But the mixed fruit deal @ 525-per-5-kg earns them 6,300 for 60 kg, which is 175 extra.

Mr B and Ms B, too, pool 30 kg apples and 30 kg oranges. At original prices, they would have earned 2,625 + 1,750 = 4,375. But the package @ 350-for-5-kg earns them only 4,200, which is 175 less.

Where did Couple A’s extra 175 come from, and where did 175 go out of Couple B’s original earnings?

#Puzzle 27.2.
#Puzzle 27.2.
Mailbox: Last week’s solvers:

#Puzzles 26.1 & 26.2

Dear Sir, 

The tortoise ran the distance from the midpoint of the avenue to the finish at twice its original speed. The hare reached the end of the avenue in both scenarios and his speed remains the same. 

Since the tortoise's speed has doubled, he would have run twice the distance, the time being the same. Hence the distance from the end of avenue to the finish is the same as the distance from the midpoint of the avenue to its end point i.e. 30 × 25 = 750 m. 

This is also the distance between the hare and the tortoise when the tortoise won the race. 

All other information about the tortoise's current position, his distance from the 10th and 11th pairs of trees and the hypothetical case of his turning back is redundant, and is given only to confuse us. 

Sunita Gupta, Delhi 

Smart solutions: Sunita Gupta (Delhi), Sunita & Naresh Dhillon (Gurgaon), Shishir Gupta (Indore), Harshit Arora (Delhi)
Longer solutions: Dr S Anju Iyengar (Faridabad), Sarang Sule (Mumbai), Dr Nakul Makkar (Noida), Mayobhav Pathak (Gurgaon), Amardeep Singh (Meerut), Jasvinder Singh (Nabha), Vasu Handa (Sonipat), Lucky Singh Randhawa (Mandawali, Delhi), Rahul Agarwal (Bay Area, California)

Problematics will be back next week. Please send in your replies by Friday noon to problematics@hindustantimes.com

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  • ABOUT THE AUTHOR
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    Puzzles Editor Kabir Firaque is the author of the weekly column Problematics. A journalist for three decades, he also writes about science and mathematics.

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