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.
Answers
Given : 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.
Solution:
Let the numerator and denominator of the fraction be x and y.
Then , fraction = numerator / denominator = x/y
Condition : 1
x = y – 4
x – y = − 4 …………..(1)
Condition : 2
y + 1 = 8(x - 2)
y + 1 = 8x – 16
y + 1 + 16 = 8x
y + 17 = 8x
8x – y = 17 ……….(2)
On Subtracting equation (2) from equation (1), we obtain :
x – y = - 4
8x – y = 17
(-) (+) (-)
------------------
−7x = − 21
x = 21/7
x = 3
On putting x = 3 in eq (1) we obtain :
x – y = − 4
3 – y = – 4
3 + 4 = y
y = 3 + 4
y = 7
Now, Fraction = x/y = 3/7
Hence the fraction is 3/7.
Hope this answer will help you…
Some more questions from this chapter :
The denominator of a fraction is 1 more than twice its numerator. If the sum of the fraction and its reciprocal is 34/15. Find the fraction.
(Class 10 Maths Sample Question Paper)
https://brainly.in/question/2368643
The difference between two numbers is 26 and one number is three times the other.Find them.
https://brainly.in/question/17204165
Answer:
Step-by-step explanation:
Solution :-
Let the numerator be x.
And the denominator be y.
According to the Question,
⇒ x = y - 4
⇒ x = y - 4 ...(i)
⇒ 8(x - 2) = y + 1
⇒ 8x - y = 17 ....(ii)
Putting the value of Eq (i), we get
⇒ 8(y - 4) - y = 17
⇒ 8y - 32 - y = 17
⇒ 7y = 49
⇒ y = 7
Putting y's value in Eq (i), we get
⇒ x = y - 4
⇒ x = 7 - 4
⇒ x = 3
Hence, the required fraction is 3/7.