Question

(iii) In a poultry form 1,83,692 eggs were collected during a year. Out of
there 13,696 egg: were cracked so could not be sold. How many eggs
could be sold in .ll?
21 und 2​

Answer 1

Answer:

We solve this problem by turning the question into two equations. (When the question was set in ancient China they were not able to do this since this technique had not yet been invented. And perhaps this is why there are, in fact, four solutions.)

If the number of cocks, hens and chicks are x, y and z. Then we have

(A) x + y + z = 100

(B) 5x + 3y + z/3 = 100Multiply (B) by 3 to get (C) 15x + 9y + z = 300. From (A) we know that z = 100 – x – y. Substitute that expression for the z in (C) and we get an equation that simplifies to 14x + 8y = 200. We can assume from the question that since we are dealing in animals, we cannot buy fractions of animals. In other words we are looking for whole number solutions, and the only way to find them is trial and error. There are four solutions

x = 0 and y = 25, in which case z = 75

x = 4 and y = 18, in which case z = 78

x = 8 and y = 11, in which case z = 81

x = 12 and y = 4, in which case z = 84

The answer is that you would buy either zero cocks, 25 hens and 75 chicks, OR 4 cocks, 18 hens and 78 chicks, OR 8 cocks, 14 hens and 78 chicks, OR 12 cocks, 4 hens and 84 chicks.

NOTE: There was originally a typo above (as noticed by several readers in the comments). This has now been changed. Also, in response to the comments below, there are other ways to find the results than by trial and error, but these rely on some technical maths, such as remembering an algorithm, which is beyond the general reader.

Step-by-step explanation:

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Answer 2

Answer:

Total no. of eggs collected - 1,83,692 eggs

Total no. eggs cracked - 13,696 eggs

Total no. of eggs that can be sold

= 1,83,692 - 13,696 eggs

= 1,69,996 eggs

$183692 - 13696 = 169996 \: eggs$

Therefore, 1,69,996 eggs can

be sold.