The following three FIs dominate a local market and their total assets are given below. $$\begin{array} { | c | r | }
\hline \text { Institution } & \text { Asset Size } \
\hline \text { Bank A } & \text { \$50 million } \
\hline \text { Bank B } & \text { \$60 million } \
\hline \text { Bank C } & \text { \$90 million } \
\hline
\end{array}$$ If Bank C agrees to be purchased by Banks A and B, what proportion of assets of Bank C should be taken by Banks A and B, respectively in order to have equal post-merger assets?
A)52 percent and 48 percent.
B)50 percent and 40 percent.
C)56 percent and 44 percent.
D)40 percent and 50 percent.
E)45 percent and 55 percent.

Question

The following three FIs dominate a local market and their total assets are given below. $$\begin{array} { | c | r | } 
\hline \text { Institution } & \text { Asset Size } \
\hline \text { Bank A } & \text { \$50 million } \
\hline \text { Bank B } & \text { \$60 million } \
\hline \text { Bank C } & \text { \$90 million } \
\hline
\end{array}$$ If Bank C agrees to be purchased by Banks A and B, what proportion of assets of Bank C should be taken by Banks A and B, respectively in order to have equal post-merger assets?
A)52 percent and 48 percent.
B)50 percent and 40 percent.
C)56 percent and 44 percent.
D)40 percent and 50 percent.
E)45 percent and 55 percent.

Quizplus · Accepted Answer

To have equal post-merger assets, the assets of Bank A and Bank B after acquiring portions of Bank C should be equal. Let x be the proportion of Bank C's assets acquired by Bank A, then Bank B acquires (1-x). The equation is: 50 + 90x = 60 + 90(1-x). Solving gives x = 0.56, so Bank A should acquire 56% and Bank B 44%.

The Following Three FIs Dominate a Local Market and Their