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If the numerator of a fraction is increased by 150% and the denominator of the fraction is increased by 300%, the resultant fraction is 5/18. What is original fraction?
- a)4/9
- b)4/5
- c)8/9
- d)8/11
Correct answer is option 'A'. Can you explain this answer?
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Most Upvoted Answer
If the numerator of a fraction is increased by 150% and the denominat...
Given:
- The numerator of a fraction is increased by 150%.
- The denominator of the fraction is increased by 300%.
- The resultant fraction is 5/18.
To find:
- The original fraction.
Solution:
Let's assume the original fraction is a/b.
Step 1: Express the given information in terms of the original fraction:
- The numerator of the new fraction is increased by 150%, which means it becomes (a + 1.5a) = 2.5a.
- The denominator of the new fraction is increased by 300%, which means it becomes (b + 3b) = 4b.
- The resultant fraction is 5/18.
Step 2: Set up an equation using the given information:
2.5a/4b = 5/18
Step 3: Simplify the equation:
Multiply both sides of the equation by 4b and 18 to eliminate the denominators:
2.5a * 18 = 5 * 4b
45a = 20b
Step 4: Simplify further:
Divide both sides of the equation by 5 to simplify the coefficients:
9a = 4b
Step 5: Determine the relationship between a and b:
Since a and b are both positive integers, the only way for 9a to be equal to 4b is if a = 4 and b = 9.
Step 6: Check the solution:
Substitute the values of a and b into the original equation:
2.5(4)/(4)(9) = 5/18
10/36 = 5/18
The equation is satisfied, which means the original fraction is 4/9.
Therefore, the correct answer is option A) 4/9.
- The numerator of a fraction is increased by 150%.
- The denominator of the fraction is increased by 300%.
- The resultant fraction is 5/18.
To find:
- The original fraction.
Solution:
Let's assume the original fraction is a/b.
Step 1: Express the given information in terms of the original fraction:
- The numerator of the new fraction is increased by 150%, which means it becomes (a + 1.5a) = 2.5a.
- The denominator of the new fraction is increased by 300%, which means it becomes (b + 3b) = 4b.
- The resultant fraction is 5/18.
Step 2: Set up an equation using the given information:
2.5a/4b = 5/18
Step 3: Simplify the equation:
Multiply both sides of the equation by 4b and 18 to eliminate the denominators:
2.5a * 18 = 5 * 4b
45a = 20b
Step 4: Simplify further:
Divide both sides of the equation by 5 to simplify the coefficients:
9a = 4b
Step 5: Determine the relationship between a and b:
Since a and b are both positive integers, the only way for 9a to be equal to 4b is if a = 4 and b = 9.
Step 6: Check the solution:
Substitute the values of a and b into the original equation:
2.5(4)/(4)(9) = 5/18
10/36 = 5/18
The equation is satisfied, which means the original fraction is 4/9.
Therefore, the correct answer is option A) 4/9.
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Community Answer
If the numerator of a fraction is increased by 150% and the denominat...
Let the fraction be n/d & after that it becomes 2.5n/4d = 5/18, so we get the result 4/9
Hence, the correct option is (a).
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If the numerator of a fraction is increased by 150% and the denominator of the fraction is increased by 300%, the resultant fraction is 5/18. What is original fraction?a)4/9b)4/5c)8/9d)8/11Correct answer is option 'A'. Can you explain this answer?
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