Question

The numerator and the denominator of a rational number are in the ratio 7:5. When 4 is added to both
the numerator and denominator, the ratio becomes 5:4. What is the rational number?

Answer 1

Answer:

Two numbers are in the ratio of 5:7

Let the rational between two numbers be x.

Hence the two numbers are 5x and 7x

if 5 is added to each of them, then their ratio becomes 3:4

After addition of 5 in the number the number becomes 5x + 5 and 7x + 5. The ratio between the numbers

(5x + 5) / (7x + 5) = 3/ 4

Cross multiplication

3 (7x + 5) = 4 (5x + 5)

21x + 15 = 20x + 20

21x - 20x =20 - 15

x = 5

The rational is 5. Hence the numbers are

One number = 5x = 5 × 5 = 25

Other number = 7x = 5 × 7= 35

Thus, the two numbers are 25 and 35

Answer the two numbers are 25 and 35