The ratio of two numbers is 2 : 3. If two is subtracted from the first numberand 8 from the second, the ratio becomes the reciprocal of the original ratio.Find the numbers.
Let the two numbers be 2x and 3x.
If two is subtracted from the first number and 8 from the second, the ratio becomes the reciprocal of the original ratio.
⇒ 
⇒ 2 (2x – 2) = 3 (3x – 8)
⇒ 4x – 4 = 9x – 24
⇒ 9x – 4x = 24 – 4
⇒ 5x = 20 ∴ x = 4
Substituting the value of x = 4,
The two numbers are 8 and 12.
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