CAT 1997 — QA Question 53
Answer the next 2 questions based on the following information.
A thief, after committing the burglary, started fleeing at 12 noon, at a speed of 60 km/hr. He was then chased by a policeman X. X started the chase, 15 min after the thief had started, at a speed of 65 km/hr.
Direction: Each of these items has a question followed by two statements, I and II. Mark the answer
1. if the question can be answered with the help of one statement alone.
2. if the question can be answered with the help of any one statement independently.
3. if the question can be answered with the help of both statements together.
4. if the question cannot be answered even with the help of both statements together.
What is the area bounded by the two lines and the coordinate axes in the first quadrant?
I. The lines intersect at a point which also lies on the lines 3x – 4y = 1 and 7x – 8y = 5.
II. The lines are perpendicular, and one of them intersects the Y-axis at an intercept of 4.
Answer & solution
Answer: 3
If we solve the two given equations, we get the point of intersection as (3, 2). Let A = (3, 2). The lines of our interest (let it be L1 and L2) also pass through A. One of the lines passes through (0, 4). Let L1 passes through (0, 4), but it also passes through (3, 2). Hence, we can find the slope of L2 (which is equal to – ). Hence, slope of L2 will be since L1 and L2 are perpendicular.
Hence, equations of L1 and L2 can be obtained by using slope point form. (Students! we need not really find out the equations.) After getting both the equations, we can find the area bounded by L1 and L2 and coordinate axes.