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Divide 50 into two parts such that the sum of their reciprocals is 1/12. The numbers are
- a)24, 26
- b)28, 22
- c)27,23
- d)20, 30
Correct answer is option 'D'. Can you explain this answer?
Most Upvoted Answer
Divide 50 into two parts such that the sum of their reciprocals is 1/1...
let one number be x
the other number will be 50-x
1/x + 1/(50-x)= 1/12
50-x+x = x(50-x)/12
600 = 50x-x^2
x^2-50x+600=0
x^2-30x-20x+600=0
x(x-30)-20(x-30)=0
(x-30)(x-20)=0
x= 20or 30 thenumbers are 20 and 30
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Divide 50 into two parts such that the sum of their reciprocals is 1/1...
Solution:
Let the two parts be x and y.
According to the given condition, we have:
1/x + 1/y = 1/12
Multiplying both sides by 12xy, we get:
12y + 12x = xy
Rearranging the terms, we get:
xy - 12x - 12y = 0
Adding 144 on both sides, we get:
xy - 12x - 12y + 144 = 144
Factorizing the left-hand side, we get:
(x - 12)(y - 12) = 144
Now, we need to find two numbers whose product is 144 and whose sum is 50. By trial and error, we find that the numbers are 20 and 30.
Therefore, the two parts are 20 and 30.
The steps can be summarised as follows:
1. Let the two parts be x and y.
2. Write the equation according to the given condition: 1/x + 1/y = 1/12
3. Multiply both sides by 12xy.
4. Rearrange the terms to get: xy - 12x - 12y = 0
5. Add 144 on both sides.
6. Factorize the left-hand side to get: (x - 12)(y - 12) = 144
7. Find two numbers whose product is 144 and whose sum is 50.
8. The two parts are 20 and 30.
Let the two parts be x and y.
According to the given condition, we have:
1/x + 1/y = 1/12
Multiplying both sides by 12xy, we get:
12y + 12x = xy
Rearranging the terms, we get:
xy - 12x - 12y = 0
Adding 144 on both sides, we get:
xy - 12x - 12y + 144 = 144
Factorizing the left-hand side, we get:
(x - 12)(y - 12) = 144
Now, we need to find two numbers whose product is 144 and whose sum is 50. By trial and error, we find that the numbers are 20 and 30.
Therefore, the two parts are 20 and 30.
The steps can be summarised as follows:
1. Let the two parts be x and y.
2. Write the equation according to the given condition: 1/x + 1/y = 1/12
3. Multiply both sides by 12xy.
4. Rearrange the terms to get: xy - 12x - 12y = 0
5. Add 144 on both sides.
6. Factorize the left-hand side to get: (x - 12)(y - 12) = 144
7. Find two numbers whose product is 144 and whose sum is 50.
8. The two parts are 20 and 30.
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Divide 50 into two parts such that the sum of their reciprocals is 1/12. The numbers area)24, 26b)28, 22c)27,23d)20, 30Correct answer is option 'D'. Can you explain this answer?
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Divide 50 into two parts such that the sum of their reciprocals is 1/12. The numbers area)24, 26b)28, 22c)27,23d)20, 30Correct answer is option 'D'. Can you explain this answer? for CA Foundation 2025 is part of CA Foundation preparation. The Question and answers have been prepared according to the CA Foundation exam syllabus. Information about Divide 50 into two parts such that the sum of their reciprocals is 1/12. The numbers area)24, 26b)28, 22c)27,23d)20, 30Correct answer is option 'D'. Can you explain this answer? covers all topics & solutions for CA Foundation 2025 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Divide 50 into two parts such that the sum of their reciprocals is 1/12. The numbers area)24, 26b)28, 22c)27,23d)20, 30Correct answer is option 'D'. Can you explain this answer?.
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