2ax + 5y = 17 4x + 6by = 11 In the x-y plane, the above two straight

A moderately difficult question on Co-ordinate geometry, made to look more difficult by the presence of additional variables, a, b and c. However, if you are strong with your concepts on the topic, you’ll mostly sail through this question smoothly.

If a line passes through a point, the co-ordinates of the point should satisfy the equation of the straight line.

If two lines intersect at a point, the co-ordinates of the point should satisfy the equations of both the lines.

Since the two lines intersect at (3,c), we can rewrite the given equations as:

6a + 5c = 17

12 + 6bc = 11.

From the above equations, it’s not hard to figure out that, if we have the value of c, we can find out unique values of a and b from the individual equations and hence find out a unique value of a+b.

Statement I gives the value of c. This is sufficient. Possible answer options are A or D. Answer options B, C and E can be eliminated.

Reorganising the equation given in statement II, we have,

y = -\(\frac{2ax}{5}\) + \(\frac{17}{5}\).

\(\frac{17}{5}\), which is 3.4, represents the y-intercept of the line 2ax + 5y = 17, when written in the y = mx + c form. So, the statement is reiterating what we already know and not giving us any data about c.

So, statement II alone is insufficient. Answer option D can be eliminated.
The correct answer option is A.

Hope this helps!