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The numerator of a fraction is 4 less than the denominator. If the numerator is decreased by 2 and denominator is increased by 1, then the denominator is eight times the numerator. Find the fraction.
- a)4/12
- b)3/13
- c)3/7
- d)11/7
Correct answer is option 'C'. Can you explain this answer?
Verified Answer
The numerator of a fraction is 4 less than the denominator. If the num...
Let the numerator be x & denominator be y
Fraction = numerator/denominator = x/y
ATQ
CASE 1 :
x = y - 4
x- y = - 4 …………..(1)
Fraction = numerator/denominator = x/y
ATQ
CASE 1 :
x = y - 4
x- y = - 4 …………..(1)
CASE 2 :
8(x - 2) = y + 1
8x - 16 = y + 1
8x - y = 17………... (2)
8(x - 2) = y + 1
8x - 16 = y + 1
8x - y = 17………... (2)
On Subtracting equation (2) from (1)
x - y = - 4
8x - y = 17
(-) (+) (-)
----------------
-7x = -21
Transposing (-7) to R.H.S, we get
x = 21/7
⇒ x = 3
Put x = 3 in equation 1,
x - y = - 4
3 - y = - 4
y = 3 + 4 = 7
y = 7
x - y = - 4
8x - y = 17
(-) (+) (-)
----------------
-7x = -21
Transposing (-7) to R.H.S, we get
x = 21/7
⇒ x = 3
Put x = 3 in equation 1,
x - y = - 4
3 - y = - 4
y = 3 + 4 = 7
y = 7
Therefore, x = 3 and y = 7
⇒ Fraction = x/y = 3/7
Hence, the fraction is 3/7.
⇒ Fraction = x/y = 3/7
Hence, the fraction is 3/7.
This question is part of UPSC exam. View all Class 8 courses
Most Upvoted Answer
The numerator of a fraction is 4 less than the denominator. If the num...
To solve this problem, let's first assign variables to the numerator and denominator of the fraction. Let's say the numerator is represented by 'n' and the denominator is represented by 'd'.
Step 1: Translate the given information into equations.
According to the problem, the numerator is 4 less than the denominator. This can be written as:
n = d - 4
Step 2: Translate the second piece of information into an equation.
If the numerator is decreased by 2 and the denominator is increased by 1, then the denominator is eight times the numerator. This can be written as:
d + 1 = 8(n - 2)
Step 3: Solve the system of equations.
We can substitute the value of 'n' from the first equation into the second equation:
d + 1 = 8((d - 4) - 2)
Simplifying this equation:
d + 1 = 8(d - 6)
d + 1 = 8d - 48
48 + 1 = 8d - d
49 = 7d
d = 49/7
d = 7
Now that we have found the value of 'd', we can substitute it back into the first equation to find the value of 'n':
n = 7 - 4
n = 3
Step 4: Write the fraction.
The fraction is n/d, which is 3/7.
Therefore, the correct answer is option C) 3/7.
Step 1: Translate the given information into equations.
According to the problem, the numerator is 4 less than the denominator. This can be written as:
n = d - 4
Step 2: Translate the second piece of information into an equation.
If the numerator is decreased by 2 and the denominator is increased by 1, then the denominator is eight times the numerator. This can be written as:
d + 1 = 8(n - 2)
Step 3: Solve the system of equations.
We can substitute the value of 'n' from the first equation into the second equation:
d + 1 = 8((d - 4) - 2)
Simplifying this equation:
d + 1 = 8(d - 6)
d + 1 = 8d - 48
48 + 1 = 8d - d
49 = 7d
d = 49/7
d = 7
Now that we have found the value of 'd', we can substitute it back into the first equation to find the value of 'n':
n = 7 - 4
n = 3
Step 4: Write the fraction.
The fraction is n/d, which is 3/7.
Therefore, the correct answer is option C) 3/7.
Community Answer
The numerator of a fraction is 4 less than the denominator. If the num...
3/7 is the correct answer because 3 is 4 times smaller than 7 and 11/7 is not the answer because 11 is 4 times larger than 7 where as in the question it said that the numerator should be less than denominator by 4 times.
please upvote to me and my answer and also start following me!!!
please upvote to me and my answer and also start following me!!!
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The numerator of a fraction is 4 less than the denominator. If the numerator is decreased by 2 and denominator is increased by 1, then the denominator is eight times the numerator. Find the fraction.a)4/12b)3/13c)3/7 d)11/7Correct answer is option 'C'. Can you explain this answer?
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