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Question
The ratio of two numbers is `(2)/(5)`. If 4 is added in first and 32 is subtracted from the second, the ratio becomes the reciprocal of the original ratio. Find the numbers.
Solution
Let the two numbers be x and y.
According to given information, we have
`x/y = (2)/(5)`
⇒ 5x - 2y = 0
⇒ 5x - 2y = 0 ....(i)
And,
`(x + 4)/(y - 32) = (5)/(2)`
⇒ 2x + 8 = 5y - 160
⇒ 2x - 5y = -168 ....(ii)
Multiplying eqn. (i) by 5 and eqn. (ii) by 2, we get
25x - 10y = 0 ....(iii)
4x - 10y = -336 ....(iv)
Subtracting eqn. (iv) from eqn. (iii), we get
21x = 336
⇒ x = 16
⇒ 5(16) - 2y = 0
⇒ 80 - 2y = 0
⇒ 2y = 80
⇒ y = 40
Thus, the numbers are 16 and 40.
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