Directions: Q. 16 to 20 |
Amit is planning to buy a house and the layout is given below. The design and the measurement has been made such that areas of two bedrooms and kitchen together is 95 sq m. |
Based on the above information, answer the following questions: |
A) \[2x+y=19,x-y=13\]
B) \[2x+y=19,x+y=13\]
C) \[2x-y=13,x+y=19\]
D) \[2x-y=19,x+y=13\]
Correct Answer: B
Solution :
From the given figure we see that area of two bedrooms \[=2\left( 5x \right)=10x\,{{m}^{2}}\] |
Area of kitchen \[=5\times y=5y\,{{m}^{2}}\] |
According to the question, |
Area of the two bedrooms and area of kitchen = 95 |
\[\therefore \,\,\,10x+5y=95\] |
\[\Rightarrow \,\,\,\,2x+y=19\] |
[divide both sides by 5] ... (i) |
Also, length of the home =15 cm |
\[\therefore \,\,\,x+2+y=15\,\,\Rightarrow \,x+y=13\] ...(ii) |
Hence, pair of linear equations is |
\[2x+y=19\]and \[x+y=13\] |
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