IPMAT Question Paper 2021 | IPM Indore Quantitative Ability

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Question 25 : The x-intercept of the line that passes through the intersection of the lines x + 2y = 4 and 2x + 3y = 6, and is perpendicular to the line 3x – y = 2 is

1. 2
2. 0.5
3. 4
4. 6

Video Explanation

Explanatory Answer

First we find the intersection of the lines x + 2y = 4 and 2x + 3y = 6

Multiplying equation [1] by 2 and subtracting from [2] we get
y = 2
Putting y = 2 in equation [1] we get
x + 2(2) = 4
Or x = 0
So the point of intersection of the two lines is (0,2)
Now for the line that passes through (0,2) and is perpendicular to the line 3x – y = 2.
The line perpendicular to the line 3x – y = 2 is of the form x + 3y = k

The line which is of the form x + 3y = k and also passes through the point (0,2) is
(0) + 3(2) = k
Or k = 6

Then the line becomes x + 3y = 6 and its x intercept is the value when y = 0
So putting y = 0 we get the value of x-intercept as 6

The question is " The x-intercept of the line that passes through the intersection of the lines x + 2y = 4 and 2x + 3y = 6, and is perpendicular to the line 3x – y = 2 is "

Hence, the answer is '6'

Choice D is the correct answer.

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