# 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.

**Solution:**

Let the numerator of the rational number be x.

Therefore, its denominator will be x + 8.

The rational number will be x / x + 8.

Thus, according to the question we get

(x + 17) / (x + 8 - 1) = 3/2

(x + 17) / (x + 7) = 3/2

Cross-multiplying, we get

2(x + 17) = 3(x + 7)

2x + 34 = 3x + 21

34 - 21 = 3x - 2x

13 = x,

Hence x + 8 = 21

Thus, the numerator is 13 and the denominator = 21

Therefore, the rational number is equal to 13/21

**Video Solution:**

## 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.

### NCERT Solutions Class 8 Maths - Chapter 2 Exercise 2.6 Question 7

**Summary:**

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. The rational number so obtained is 13/21.