Question : If $\frac{A}{L}+\frac{M}{B}=1$ and $\frac{B}{M}+\frac{N}{C}=1$, then the value of $\frac{L}{A}+\frac{C}{N}$ is:
Option 1: $\frac{B}{M}$
Option 2: 0
Option 3: 1
Option 4: $\frac{M}{B}$
Correct Answer: 1
Solution :
Given: $\frac{A}{L}+\frac{M}{B}=1$............................(equation 1)
$\frac{B}{M}+\frac{N}{C}=1$.................................(equation 2)
Now,
$\frac{A}{L}+\frac{M}{B}=1$
⇒ $\frac{A}{L}=\frac{B-M}{B}$
⇒ $\frac{L}{A}=\frac{B}{B-M}$
Similarly, $\frac{C}{N}=\frac{M}{M-B}$
Putting the values in $\frac{L}{A} + \frac{C}{N}$, we get:
$\frac{L}{A} + \frac{C}{N} =\frac{B}{B-M}+\frac{M}{M-B} $
$⇒\frac{L}{A} + \frac{C}{N} =\frac{B}{B-M}-\frac{M}{B-M} $
$\therefore\frac{L}{A} + \frac{C}{N} =\frac{B-M}{B-M}=1$
Hence, the correct answer is 1.
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