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.
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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.
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