Question

positive number is 5 times another number. If 21 is added to both the numbers, then one of the new numbers becomes twice the other new number. What are the numbers?


The denominator of a rational number is greater than its numerator by 8. If the numerator is increased by 17 and the denominator is decreased by 1, the number obtained is 3/2. Find the rational number.​

Answer 1

Step-by-step explanation:

Question 1 :-

Let one of the positive number be x then other number will be 5x.

According to the question,

5x + 21 = 2(x + 21)

⇒ 5x + 21 = 2x + 42

⇒ 5x – 2x = 42 – 21

⇒ 3x = 21

⇒ x = 7

One number = x = 7

Other number = 5x = 5×7 = 35

The two numbers are 7 and 35.

Question 2 :-

Let the numerator be x then denominator will be (x + 8)

According to the question,

(x + 17)/(x + 8 – 1) = 3/2

⇒ (x + 17)/(x + 7) = 3/2

⇒ 2(x + 17) = 3(x + 7)

⇒ 2x + 34 = 3x + 21

⇒ 34 – 21 = 3x – 2x

⇒ 13 = x

The rational number is x/(x + 8)

= 13/21