Question

Two numbers are in the ratio 7 : 9. If each number is increased by 6,

the new ratio becomes 5 : 6. Find the original numbers.​

Answer 1

Answer:

The original numbers are 14 and 18.

Step-by-step explanation:

Let x and y be the two numbers.

By tye question,

x : y = 7 : 9

→ x/y = ⁷/9

→9x = 7y

→ y = 9x/7

Now,

(x + 6)/(y + 6) = ⅚

→ 6 (x+ 6) = 5 (y+ 6)

→ 6x + 36 = 5y + 30

→ 6x + 6 = 5 × (9x/7)

→ 6x + 6 = 45x /7

→ 7 (6x + 6) = 45x

→ 42x + 42 = 45x

→ 42 = 3x

→ x = 14.

Then, y = 9x/7

→ y = 9 × 14 / 7

→ y = 18.