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The numerator of a rational number is 4 less than the denominator. If the numerator is increased by 15 and denominator is decreased by 4, we get 6. Find the rational number?
- a)1/5
- b)2/7
- c)3/7
- d)5/9
- e)None of these
Correct answer is option 'C'. Can you explain this answer?
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Verified Answer
The numerator of a rational number is 4 less than the denominator. If ...
let the fraction is (p-4)/p
now, (p -4 + 15)/(p-4) = 6
we get p = 7
so fraction = 3/7
now, (p -4 + 15)/(p-4) = 6
we get p = 7
so fraction = 3/7
Most Upvoted Answer
The numerator of a rational number is 4 less than the denominator. If ...
Given information:
- Numerator of a rational number is 4 less than the denominator.
- If the numerator is increased by 15 and the denominator is decreased by 4, we get 6.
Let's use algebra to solve for the rational number.
Let the denominator be x.
Then the numerator is x - 4.
The rational number can be represented as (x - 4)/x.
When the numerator is increased by 15 and the denominator is decreased by 4, we get the following equation:
(x - 4 + 15)/(x - 4 - 4) = 6
Simplifying the equation, we get:
(x + 11)/(x - 8) = 6
x + 11 = 6(x - 8)
x + 11 = 6x - 48
59 = 5x
x = 59/5
So the denominator is 59/5.
The numerator is x - 4, which is (59/5) - 4 = 39/5.
Therefore, the rational number is (39/5)/(59/5), which simplifies to 39/59.
Thus, the correct answer is option (c) 3/7.
- Numerator of a rational number is 4 less than the denominator.
- If the numerator is increased by 15 and the denominator is decreased by 4, we get 6.
Let's use algebra to solve for the rational number.
Let the denominator be x.
Then the numerator is x - 4.
The rational number can be represented as (x - 4)/x.
When the numerator is increased by 15 and the denominator is decreased by 4, we get the following equation:
(x - 4 + 15)/(x - 4 - 4) = 6
Simplifying the equation, we get:
(x + 11)/(x - 8) = 6
x + 11 = 6(x - 8)
x + 11 = 6x - 48
59 = 5x
x = 59/5
So the denominator is 59/5.
The numerator is x - 4, which is (59/5) - 4 = 39/5.
Therefore, the rational number is (39/5)/(59/5), which simplifies to 39/59.
Thus, the correct answer is option (c) 3/7.
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The numerator of a rational number is 4 less than the denominator. If the numerator is increased by 15 and denominator is decreased by 4, we get 6. Find the rational number?a)1/5b)2/7c)3/7d)5/9e)None of theseCorrect answer is option 'C'. Can you explain this answer?
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