| Directions: (6 - 10) |
| Deepa rides her car at 25 km/hr. She has to spend Rs 2 per km on diesel and if she rides it at a faster speed of 40 km/her, the diesel cost increases to Rs 5 per km. She has Rs 100 to spend on diesel. Let she travels x kms with speed 25 km/h and y kms with speed 40 km/hr. The feasible region for the LPP is shown below : |
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| Based on the above information, answer the following questions : |
A) \[\left( \frac{40}{3},\frac{50}{3} \right)\]
B) \[\left( \frac{50}{3},\frac{40}{3} \right)\]
C) \[\left( \frac{-50}{3},\frac{40}{3} \right)\]
D) \[\left( \frac{-50}{3},\frac{-40}{3} \right)\]
Correct Answer: B
Solution :
Let B(x, y) be the point of intersection of the given lines \[2x+5y=100~\] ...(i) And \[\frac{x}{25}+\frac{y}{40}=1\] \[\Rightarrow \,\,\,8x+5y=20\] Solving (i) and (ii), we get \[x=\frac{50}{3},\,\,\,y=\frac{40}{3}\] \[\therefore \] The point of intersection \[B(x,y)=\left( \frac{50}{3},\frac{40}{3} \right)\]
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