Advertisements
Advertisements
Question
In a certain positive fraction, the denominator is greater than the numerator by 3. If 1 is subtracted from the numerator and the denominator both, the fraction reduces by `1/14`. Find the fraction.
Solution
Let the numerator be 'x'
The denominator be 'x + 3'
So the fraction is `x/(x+3)`
According to the question,
`(x - 1)/(x + 3 - 1) = x/(x + 3) - 1/14`
Firstly let us simplify RHS
`(x - 1)/(x + 2) = (14x - x - 3)/(14 (x + 3))`
`(x - 1)/(x + 2) = (13x - 3)/(14x + 42)`
By cross-multiplying, we get
(x – 1)(14x + 42) = (x + 2)(13x – 3)
14x2 + 42x – 14x – 42 = 13x2 – 3x + 26x – 6
14x2 + 42x – 14x – 42 – 13x2 + 3x – 26x + 6 = 0
x2 + 5x – 36 = 0
Let us factorize,
x2 + 9x – 4x – 36 = 0
x(x + 9) – 4(x + 9) = 0
(x + 9)(x – 4) = 0
So,
(x + 9) = 0 or (x – 4) = 0
x = – 9 or x = 4
So the value of x = 4 ...[Since, – 9 is a negative number]
When substitute the value of x = 4 in the fraction `x/(x + 3)`, we get
`4/(4 + 3) = 4/7`
∴ The required fraction is `4/7`
APPEARS IN
RELATED QUESTIONS
The sum S of n successive odd numbers starting from 3 is given by the relation: S = n(n + 2). Determine n, if the sum is 168.
One year ago, a man was 8 times as old as his son. Now his age is equal to the square of his son’s age. Find their present ages.
The age of a father is twice the square of the age of his son. Eight years hence, the age of the father will be 4 years more than three times the age of the son. Find their present ages.
Mr. Mehra sends his servant to the market to buy oranges worth Rs. 15. The servant having eaten three oranges on the way, Mr. Mehra pays Rs. 25 paise per orange more than the market price. Taking x to be the number of oranges which Mr. Mehra receives, form a quadratic equation in x. Hence, find the value of x.
A hotel bill for a number of people for overnight stay is Rs. 4800. If there were 4 people more, the bill each person had to pay, would have reduced by Rs. 200. Find the number of people staying overnight.
Rs. 6500 was divided equally among a certain number of persons. Had there been 15 persons more, each would have got Rs. 30 less. Find the original number of persons.
Mohan takes 16 days less than Manoj to do a piece of work. If both working together can do it in 15 days, in how many days will Mohan alone complete the work?
Two years ago, a man’s age was three times the square of his son’s age. In three years time, his age will be four times his son’s age. Find their present ages.
The ages of two sisters are 11 years and 14 years. In how many years’ time will the product of their ages be 304?
₹ 320 were divided equally among 8 children. If 2 more children join them, each will get, how many rupees more or less?
