A man has 25 cows. All cows are numbered 1 to 25. All cows provide as many liters of milk as their number. That is, cows of number 5 give 5 liters and cows of number 8 provide 8 liters of milk.
The man has 5 sons. Each son has to give five cows. However, each son should get the same amount of milk.
So, what number of five cows should be given to each son?
Who should be inteligent.
?
Answers
Answer:
The serial numbers of cows given to each son is as follows.
1st Son - 1, 7, 13, 19 and 25
2nd Son - 2, 8, 14, 20 and 21
3rd Son - 3, 9, 15, 16 and 22
4th Son - 4, 10, 11, 17 and 23
5th Son - 5, 6, 12, 18 and 24
Step-by-step explanation:
The total liters of milk provided by the 25 cows are 1+2+..........+25 = 25*26/2=325 liters. As such, each son should get 5 cows to have 325 / 5 = 65 litres of milk. Now, how to solve.
Write the numbers from 1 to 25 in 5 rows as follows.
1 2 3 4 5
6 7 8 9 10
11 12 13 14 15
16 17 18 19 20
21 22 23 24 25
Then give 1st son the cows in the diagonal starting from 1. Then give 2nd son the cows on the diagonal right to it starting with 2. It has four numbers. To make it up, take the single number in left bottom. Then give 3rd son the cows on the diagonal right to the earlier one that is staring with 3. Since it has now 3 numbers, take two numbers by taking the diagonal on left bottom staring with 16 and ending with 22. And continue similar ways for 4th and 5th son.
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The share of each of the five sons will be 5 cows. The man who divided his 25cows equally so that each of his sons gets an equal number of 5cows and an equal amount of milk is intelligent.
The 1st Son will get the cows numbered as 1, 7, 13, 19, and 25;
the 2nd Son will get the cows numbered as 2, 8, 14, 20, and 21;
the 3rd Son will get the cows numbered as 3, 9, 15, 16, and 22;
the 4th Son will get the cows numbered as 4, 10, 11, 17, and 23; and
the 5th Son will get the cows numbered as 5, 6, 12, 18, and 24; respectively.
Given:
A man has 25 cows. The cows are numbered from 1 to 25. The cows provide as many liters of milk as their number.
The man divides his 25 cows among his 5 sons such that each son has 5 cows and an equal amount of milk.
To Find:
the number of cows that should be given to each son.
Solution:
We can find the solution to this problem in the following way.
The sum of any consecutive n natural numbers where a is the first term and l is the last term is given by
We shall use the relevant formulae to arrive at the solution to this problem.
We can find the following
The total amount of milk of 25 cows is
Since the share of each son is equal, the share in terms of milk of each son is
Now we can arrange the numbers from 1 to 25 in a matrix and deduce by inspection the following share of 5cows of each son as indicated by the following serial numbers of cows in their respective possession.
The 1st Son will get the cows numbered as 1, 7, 13, 19, and 25;
the 2nd Son will get the cows numbered as 2, 8, 14, 20, and 21;
the 3rd Son will get the cows numbered as 3, 9, 15, 16, and 22;
the 4th Son will get the cows numbered as 4, 10, 11, 17, and 23; and
the 5th Son will get the cows numbered as 5, 6, 12, 18, and 24; respectively.
Therefore, the share of each of the five sons will be 5 cows. The man who divided his 25cows equally so that each of his sons gets an equal number of 5cows and an equal amount of milk (65liters) is intelligent.
The 1st Son will get the cows numbered as 1, 7, 13, 19, and 25;
the 2nd Son will get the cows numbered as 2, 8, 14, 20, and 21;
the 3rd Son will get the cows numbered as 3, 9, 15, 16, and 22;
the 4th Son will get the cows numbered as 4, 10, 11, 17, and 23; and
the 5th Son will get the cows numbered as 5, 6, 12, 18, and 24; respectively.
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