When 1 is added to the numerator of a fraction it becomes 1/4 and 1 is subtracted from the denominator of that fraction it becomes 1/5. Find the fraction.a)4/19b)3/16c)5/17d)2/15e)None of theseCorrect answer is option 'B'. Can you explain this answer?

Question

Answer

Given Information:
- When 1 is added to the numerator of a fraction, it becomes 1/4.
- When 1 is subtracted from the denominator of that fraction, it becomes 1/5.

To Find: The fraction.

Solution:
Let's assume that the fraction is x/y.

According to the given information,
- (x+1)/y = 1/4 ...(1)
- x/(y-1) = 1/5 ...(2)

We need to find the value of x/y from these equations.

Let's solve equation (1) for x:
x+1 = y/4
x = y/4 - 1 ...(3)

Substitute equation (3) into equation (2) and solve for y:
(y/4 - 1)/(y-1) = 1/5
5(y/4 - 1) = y-1
5y/4 - 5 = y-1
4y - 20 = 5(y-1)
4y - 20 = 5y-5
y = 15 ...(4)

Now, substitute the value of y from equation (4) into equation (3) and solve for x:
x = 15/4 - 1
x = 11/4

Therefore, the fraction is 11/15.

Answer: The fraction is not given in the options. Hence, the correct answer is option 'E' - None of these.

Answer

Let fraction = x/y
Then (x+1)/y = 1/4
And x/(y-1) = 1/5
Solve both equations, x = 3, y = 16

Answer

When 1 is added in numerator of number 3/16 it becomes 4/16 it means 1/4 and when we subtract to denominator in 3/16 it becomes 3/15 it means 1/5 . So you solve these types of questions from gives answers because it takes less time and when you will going to create equation it will take too much time to solve

Answer

Solution:
Let the fraction be x/y.
According to the question,
(x+1)/y = 1/4 ...(i)
x/(y-1) = 1/5 ...(ii)
Multiplying both sides of equation (i) by 4y and equation (ii) by 5(y-1), we get:
4(x+1) = y ...(iii)
5x = y-1 ...(iv)
Substituting equation (iv) in equation (iii), we get:
4(x+1) = 5x-1
4x+4 = 5x-1
x = 5
Substituting x=5 in equation (iv), we get:
5y = 24
y = 24/5
Therefore, the fraction is 5/24.
Checking with the given conditions:
When 1 is added to the numerator, we get:
(5+1)/24 = 1/4
When 1 is subtracted from the denominator, we get:
5/(24-1) = 5/23
So, the correct answer is option (B) 3/16.

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