• # question_answer Case Study : Q. 1 to 5 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 $\text{95 sq}.\text{ m}$. Based on the above information, give the answer of the following questions: The pair of linear equations in two variables from this situation are: A) $2x+y=19,\,\,x+y=13$ B) $x+2y=19,\,\,x+y=18$ C) $x+y=19,\,\,x+2y=13$ D) $x+3y=19,2\,x+y=15$

 Given that, length of bedroom $=x\,m$ And breadth of bedroom $=5\,m$ $\therefore$ Area of a bedroom $=5x\,\,sq.\,m$ So, area of two bedrooms $=2\times 5x=10x\,sq.\,m$ Also, length of kitchen $=y\,m$ and breadth of kitchen $=\,5\,\,m$ $\therefore$  Area of the kitchen $=5y\,\,sq.\,m$ According to question, Areas of two bedrooms and kitchen together $=95\,\,sq.\,m$ $\therefore \,\,\,\,\,\,\,\,\,\,\,\,10x+5y=95$ $\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,2x+y=19$                     ..(1) (divide both sides by 5) According to figure, Length of a bedroom + length of bathroom + length of the kitchen = Length of the layout of the house $\therefore \,\,\,\,\,\,\,\,\,\,\,\,\,\,x+2+y=15$ $\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,x+y=13$                       ..(2) Hence, eqs. (1) and (2) represent the pair of linear equations in two variables. So, option [a] is correct.