A) \[\frac{ab-cd}{a-b}\]
B) \[\frac{ac-bd}{a+b}\]
C) \[\frac{ad-bc}{c+d}\]
D) \[\frac{ad-bc}{c-d}\]
Correct Answer: D
Solution :
| [d] Let the quantity be x. Then, \[\frac{a+x}{b+x}=\frac{c}{d}\] \[\Rightarrow \] \[(a+x)\,d=(b+x)c\] \[\Rightarrow \] \[ad+dx=bc+cx\] \[\Rightarrow \] \[ab-bc=cx-dx\] \[\Rightarrow \] \[ad-bc=x\,\,(c-d)\]\[\therefore \]\[x=\frac{ad-bc}{c-d}\] |
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