Using value of money to solve fake note puzzle

By MUNGAI KIHANYA

The Sunday Nation

Nairobi,

23 October 2016

Money has no value unless you spend it! The value is in what you spend the money on. For that reason, in every fair deal, there exists two fools. The buyer goes away thinking “what kind of fool agrees to sell such a valuable thing for such a small amount?” The seller walks away wondering “what type of fool buys such a worthless thing for so much money?” The truth is that both walk away with equal value – equivalent to the price of exchange.

With that idea in mind, we can attempt to solve a puzzle that was sent to me by Francis Kimwea. He says that it has been doing the rounds on WhatsApp. It reads: “Tom went to a shop with a fake Sh1,000 note for shopping, he bought items worth Sh800. The shopkeeper had no change and went to the next shop to borrow. He came back and gave Tom his [Sh200] change.

“Shopkeeper B realised that shopkeeper A had given him a fake Sh1,000 note for change, [so] he went [back] and was given a valid Sh1,000 note. Question: How much did shopkeeper A lose? A – 1,000; B – 1,200; C – 1,800; D – 2,000; E – 2,200; F – 2,800”

We know that Tom did not pay for the goods. The Sh1,000 note he paid with was fake and, therefore, worthless. So, at that point, the shop-owner lost (goods worth) Sh800. I will come back to this figure, but for now let us accept it as it is.

Next, the shopkeeper gave Tom Sh200 change for the purchase. This brings the total amount stolen by Tom to Sh1,000.

Somewhere in the transaction, Shopkeeper A was given Sh1,000 by B, but later, B came back for her money. So, in that exchange, the net result is nil: Sh1,000 received and Sh1,000 given back.

Therefore, the total loss incurred by shopkeeper A is Sh1,000. You can also think about it this way: Tom managed to cheat A to exchange the fake Sh1,000 for a genuine one. That’s what A was left with – a worthless piece of paper with the number 1,000 written on it.

But there is a subtle point that must be made about the items that Tom stole. In the shopkeepers inventory (the stock record), they are NOT valued at Sh800! Sh800 is the selling price; the value of inventory is based on buying price. That is, the amount the shopkeeper had paid his supplier for it.

In fact, if the shopkeeper had insured his stock, the insurance company would only compensate him for the replacement cost, not the selling price. Thus the value of the item to the shopkeeper is not Sh800 but something less. Therefore the correct answer is Sh200 [the change] plus the buying price of the items.

Since we don’t know the buying price, we cannot say what the loss is. However, we expect it to be less than Sh1,000 because buying prices are usually lower than selling prices. The conclusion, therefore is than none of the choices given is correct since none is less than Sh1,000.