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What is the weight of the fish?

What is the weight of the fish?

That day in the Srijani farm, they arranged a fishing party. As luck would have it, only Debu caught a Rohu and promptly weighed it. When the other friends asked him about the weight of the fish, Debu replied in the form of a riddle,

Let us assume the tail of the fish weighs 125 gms, the head as much as the tail and half the body, and the body weighs as much as the head and tail together. Well then, how much is the weight of the fish?

Time for you to answer: 3 minutes.

No algebra please. Just mental arithmetic and reasoning.

Solution to find the weight of the fish math puzzle

It is clear that both the other two components, body and head weights must be expressed in terms of the tail, the only known figure.

Let us first clearly state the two given statements again,

  1. head equals tail and half the body, and
  2. body equals head and tail.

It is clear by doubling all three components in the first statement that,

Twice the head equals body and twice the tail.

But body equals head and tail. So, twice the head equals on head and three tails. So,

One head equals thrice the tail and body equals four times the tail.

And the total weight of the fish,

Head + body + tail = 3 times tail + 4 times tail + 1 tail = 8 times tail = 1 kg.

Answer: Weight of the fish was 1 kg.

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