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प्रश्न
If a + c = mb and `(1)/b + (1)/d = m/c`, prove that a, b, c and d are in proportion.
उत्तर
a + c = mb and `(1)/b + (1)/d = m/c`
a + c = mb
`a/c + c/d = m` (Dividing by b)...(i)
and `(1)/b + (1)/d = m/c`
`c/b + c/d = m` (Multiplying by c)...(ii)
From (i) and (ii)
`a/b + c/b`
= `c/b + c/d`
⇒ `a/b = c/d`
Hence, a, b, c and d are proportional.
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