Question

9. DIGGING A DITCH

Here is a curious question that is more perplexing than it looks at first sight. Abraham, an infirm old man, undertook to dig a ditch for two dollars. He engaged Benjamin, an able-bodied fellow, to assist him and share the money fairly according to their capacities. Abraham could dig as fast as Benjamin could shovel out the dirt, and Benjamin could dig four times as fast as Abraham could do the shoveling.

How should they divide the money? Of course, we must assume their relative abilities for work to be the same in digging or shoveling.​

Answer 1

Concept :

• Here is a curious question that is more perplexing than it looks at first sight.

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• Abraham, an infirm old man, undertook to dig a ditch for two dollars.

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• He engaged Benjamin, an able-bodied fellow, to assist him and share the money fairly according to their capacities.

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• Abraham could dig as fast as Benjamin could shovel out the dirt, and Benjamin could dig four times as fast as Abraham could do the shoveling.

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A question raised :

• How should they divide the money?

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Solution :

• Definitely the money should be divided based on their progress how they worked

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1. Digging,
2. Shoveling.

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• We have known that who digs faster and how much they have digged.

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• Abraham receives ⅓ of 2 dollars.
• Benjamin receives ⅔ of his dollars. [That's twice more than Abraham's].

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• Abraham dig for 4 hours.
• Abraham shovel for 8 hours.
• But Benjamin can do more.

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After talking their working ratios and comparing the same, we get that Benjamin can twice mode than Abraham's money.

Answer 2

Answer:

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Question ⤵⤵

9. DIGGING A DITCH

Here is a curious question that is more perplexing than it looks at first sight. Abraham, an infirm old man, undertook to dig a ditch for two dollars. He engaged Benjamin, an able-bodied fellow, to assist him and share the money fairly according to their capacities. Abraham could dig as fast as Benjamin could shovel out the dirt, and Benjamin could dig four times as fast as Abraham could do the shoveling.

How should they divide the money? Of course, we must assume their relative abilities for work to be the same in digging or shoveling.

Answer ⤵⤵

A. should receive one-third of two dollars, and B. two-thirds. Say B. can dig all in 2 hours and shovel all in 4 hours; then A. can dig all in 4 hours and shovel all in 8 hours. That is, their ratio of digging is as 2 to 4 and their ratio of shovelling as 4 to 8 (the same ratio), and A. can dig in the same time that B. can shovel (4 hours), while B. can dig in a quarter of the time that A. can shovel. Any other figures will do that fill these conditions and give two similar ratios for their working ability. Therefore, A. takes one-third and B. twice as much-two-thirds.