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Ques:- Five farmers have 7, 9, 11, 13 & 14 apple trees, respectively in their orchards. Last year, each of them discovered that every tree in their own orchard bore exactly the same number of apples. Further, if the third farmer gives one apple to the first, and the fifth gives three to each of the second and the fourth, they would all have exactly the same number of apples. What were the yields per tree in the orchards of the third and fourth farmers?
Recent Answer : Added by John Rony On 2021-06-23 17:56:01:
So we consider the 2nd statement first. We can form an equation out of it.
14x-6=13y+3=9z+3
Using this, we can understand that the multiple of 14 and the multiple of 13 and 9 must have a difference of 9. The easiest way to ensure that is multiplying it by 9
14*9=126
13*9=117
If the 5th farmer gives 3 apples to the 4th farmer, they would have 123 and 120 apples respectively. However, we also know that the 2nd farmer has 117 apples (13*9=117, and this is a multiple of 9) if the 5th farmer gives 3 apples too the 2nd farmer, the 3rd, 4th and 5th farmers would have 120 apples each.
Now that we got 120, we should check if the first part of the question makes sense along with it. The equation would be
7a+1=11b-1=120
We know that 11*11=121 and 7*17=119. When we add 1 to 119 and subtract 1 from 121, we get 120 for each. In this way, all the farmers have 120 apples each.
Therefore, the 3rd farmer had a yield of 11 per tree and the 4th farmer had a yield of 9 per tree.
Ques:- The LCM of two numbers is 75. The GCF is 5. The sum of the numbers is 40. What are the numbers?
Recent Answer : Added by Akshay On 2022-03-09 16:46:01:
15,25
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Ques:- B – 1, B – 2 and B – 3 are three buses that travel from Mumbai to Delhi. Each bus starts at a different time and arrives at a different time. The digit in the bus number and the order of their departure of arrival is not the same. The first bus to leave Mumbai is the third bus to reach Delhi. Which is the first bus to leave Mumbai?
Recent Answer : Added by DK BOSS On 2021-07-21 15:26:32:
B1
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Ques:- The difference between a number and its three-fifth is 50. What is the number? (a) 75 (b) 100 (c) 125 (d) 80 (e) None of these
Recent Answer : Added by Admin On 2020-05-17 12:03:49:
let the no be x
then given that the difference between the number and 3/5th
of the number is 50
therefor , x-3/5x=50
2x=250
x=125 is the answer
Ques:- 40.83 x 1.02 x 1.2 = ?
Recent Answer : Added by Gowtham On 2022-09-15 16:37:20:
There should be 5(2+2+1) decimal places in the answer and the decimal place should end with 2(3*2*2=12) so the correct answer is a, no need for calculator. You can rule out all the other options because it does not satisfy this condition.
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Recent Answer : Added by Lavish Garg On 2022-08-14 16:31:11:
16
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Recent Answer : Added by N.Madhu Charan On 2022-03-09 16:35:25:
Neice
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Ques:- The cost of 17 apples, 9 oranges , 13 bananas is rs 130 , whereas cost of 13 oranges, 7 apples and 10 bananas is rs 100. find the cost of 1 apple , 1 banana and 1 orange put together?
Recent Answer : Added by Admin On 2022-09-27 18:08:58:
Let cost for apple be a Cost for banana be b and Orange be c
So by first value expression becomes 17a + 13b + 9c =130 ———-1 therefore if you further solve a = (130 – 13b – 9c)/17 ———- 2 the second expression becomes: 13c + 7a + 10b = 100 ———- 3 If you put value of a in second expression it becomes: 13c + 7[(130 – 3b – 9c)/17] +10b = 100
So we consider the 2nd statement first. We can form an equation out of it.
14x-6=13y+3=9z+3
Using this, we can understand that the multiple of 14 and the multiple of 13 and 9 must have a difference of 9. The easiest way to ensure that is multiplying it by 9
14*9=126
13*9=117
If the 5th farmer gives 3 apples to the 4th farmer, they would have 123 and 120 apples respectively. However, we also know that the 2nd farmer has 117 apples (13*9=117, and this is a multiple of 9) if the 5th farmer gives 3 apples too the 2nd farmer, the 3rd, 4th and 5th farmers would have 120 apples each.
Now that we got 120, we should check if the first part of the question makes sense along with it. The equation would be
7a+1=11b-1=120
We know that 11*11=121 and 7*17=119. When we add 1 to 119 and subtract 1 from 121, we get 120 for each. In this way, all the farmers have 120 apples each.
Therefore, the 3rd farmer had a yield of 11 per tree and the 4th farmer had a yield of 9 per tree.