1. x+3/2x-6=3/2
2. 5y-2/2y+8
3. The denominator of a rational number is greater than its numerator by 6. If the numerator is decreased by 1 and the denominator increased by 1 , the number obtained is 1/3 . Find the rational number.
4. Sum of the digits of a two digit number is 8 . When we interchange the digits , it is found that the resulting new number is less than the original number by 18 . What is the two digit number?
5. Arjun is twice as old as Shriya. Five years ago his age was three times Shriya’s age
. Find their present ages .
Answers
Step-by-step explanation:
1.=3
2. =−2
3.Let the numerator of the rational number be x.
Then, the denominator of the rational number =x+6.
It is given that the numerator is increased by 5 and the denominator is decreased by 3.
∴ the numerator of the new rational number =x+5.
Denominator of the new rational number =(x+6)−3=x+3
∴ new rational number = x+3x+5
But the new rational number is given as 45.
∴x+3x+5=45
By cross multiplying, we get,
4(x+5)=5(x+3)
⇒4x+20=5x+15
⇒4x−5x=15−20 ....[Transposing 5x to LHS. and 20 to RHS]
⇒−x=−5 or x=5
∴ numerator of the rational number is 5 and denominator = 5+6 i.e. 11.
∴ the required rational number is 11/5.
4.two digit number is 30
5.The age of Shriya = y - 5. According to the question, five years ago Arjun's age was 3 times the age of Shriya. This gives us the second relation and we obtain equation (2). Hence, the present age of Arjun is 20 years and the present age of Shriya is 10 years.
Answer:
4.two digit number is 30