Question

If x-intercept of the straight line ax+2ay=30 is 10, then the y-intercept is

• A. 5
• B. 10
• C. 15
• D. 20
• E. 30

Answer 1

The Correct Option is A

Let the equation of the straight line be: \[ ax + 2ay = 30 \] 

Step 1: Find the x-intercept 
The x-intercept is found by setting \( y = 0 \): \[ ax + 2a(0) = 30 \Rightarrow ax = 30 \Rightarrow x = \frac{30}{a} \] Given that the x-intercept is 10: \[ \frac{30}{a} = 10 \] Solving for \( a \): \[ a = \frac{30}{10} = 3 \]

Step 2: Find the y-intercept 
The y-intercept is found by setting \( x = 0 \): \[ 3(0) + 2(3)y = 30 \] \[ 6y = 30 \] \[ y = \frac{30}{6} = 5 \]

Final Answer: The y-intercept is 5.