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If p, q and r are positive integers and satisfy x = (p + q -r)/r = (p - q + r)/q = (q + r - p)/p, then the value of x is?
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If p, q and r are positive integers and satisfy x = (p + q -r)/r = (p - q + r)/q = (q + r - p)/p, then the value of x is?
A). 1/2
B). 1
C). -1/2
D). -1
1 answers
-2 vote
1
When two or more ratios are equal, each of the ratios are equal to sum of the numerators divided by the sum of the denominators, provided sum of the denominators is non-zero.
Hence, x = (p + q -r)/r = (p - q + r)/q = (q + r - p)/p
=> x = (p + q - r + p - q + r + q + r - p) / (r + q + p)
=> x = (r + q + p) / (r + q + p) = 1
p + q + r is non-zero.