Answer : Option D

Explanation :

Let the expenditures of each companies X and Y in 1996 be Rs. x crores.

And let the income of Company X in 1996 be Rs. z crores.

So that the income of Company Y in 1996 = Rs. (342 - z) crores.

Then, for Company X we have:

40 = \(\frac { Z - X } { X }\) x 100   \( \frac { 40 } { 100 } \) = \( \frac { Z } { X } \) - 1       x = \(\frac { 100Z } { 140} \) ... (i)

Also, for Company Y we have:

45 = \(\frac { (342- Z) } { X } \) X 100 \( \frac {(342- Z )} { X} \)   -1    x = \(\frac { (342 -Z) *100 } {145 } \)... (ii)

From (i) and (ii), we get:

\( \frac { 100Z } { 140} \) = \( \frac { (342-Z)*100 } { 145 } \)      z = 168.

Substituting z = 168 in (i), we get : x = 120.

 Total expenditure of Companies X and Y in 1996 = 2x = Rs. 240 crores.

Total income of Companies X and Y in 1996 = Rs. 342 crores.

 Total profit = Rs. (342 - 240) crores = Rs. 102 crores.