Advertisements
Advertisements
Question
If numerator is 2 less than denominator of a rational number and when 1 is subtracted from numerator and denominator both, the rational number in its simplest form is `1/2`. What is the rational number?
Solution
Suppose denominator of a rational number be x.
Numerator = Denominator – 2 = x – 2
According to the question,
`((x - 2) - 1)/(x - 1) = 1/2`
⇒ 2(x – 2 – 1) = x – 1
⇒ 2(x – 3) = x – 1
⇒ 2x – 6 = x – 1
⇒ 2x – x = 6 – 1
∴ x = 5
Hence, denominator = 5 and numerator = 5 – 2 = 3
Thus, the rational number is `3/5`.
APPEARS IN
RELATED QUESTIONS
The ages of Hari and Harry are in the ratio 5:7. Four years from now the ratio of their ages will be 3:4. Find their present ages.
Find a number such that when 5 is subtracted from 5 times the number, the result is 4 more than twice the number.
I am currently 5 times as old as my son. In 6 years time I will be three times as old as he will be then. What are our ages now?
I have Rs 1000 in ten and five rupee notes. If the number of ten rupee notes that I have is ten more than the number of five rupee notes, how many notes do I have in each denomination?
At a party, colas, squash and fruit juice were offered to guests. A fourth of the guests drank colas, a third drank squash, two fifths drank fruit juice and just three did not drink any thing. How many guests were in all?
There are 180 multiple choice questions in a test. If a candidate gets 4 marks for every correct answer and for every unattempted or wrongly answered question one mark is deducted from the total score of correct answers. If a candidate scored 450 marks in the test, how many questions did he answer correctly?
The numerator of a rational number is 3 less than the denominator. If the denominator is increased by 5 and the numerator by 2, we get the rational number 1/2. Find the rational number.
A lady went shopping and spent half of what she had on buying hankies and gave a rupee to a beggar waiting outside the shop. She spent half of what was left on a lunch and followed that up with a two rupee tip. She spent half of the remaining amount on a book and three rupees on bus fare. When she reached home, she found that she had exactly one rupee left. How much money did she start with?
If `x/11 = 15`, then `x = 11/15`
Solve the following:
`(3x - 8)/(2x) = 1`
