## Pair Of Linear Equations In Two Variables Class 10 Maths - Test

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** Pair Of Linear Equations In Two Variables - Test**

**1.**Half the perimeter of a garden, whose length is 4 m more than its width is 36 m . Find the dimensions of the garden(graphically). (2 Marks)

**2.**Given the linear equation $2x+3y-8=0,$ write another linear equation in two variables such that the geometrical representation of the pair is : i) intersecting lines ii) parallel lines. (2 Marks)

**3.**Solve for $x\text{\hspace{0.33em}}and\text{\hspace{0.33em}}y$ by substitution method (3 Marks)

$$\begin{array}{l}\frac{a}{x}-\frac{b}{y}=0\\ \frac{a{b}^{2}}{x}+\frac{{a}^{2}b}{y}={a}^{2}+{b}^{2}\end{array}$$

**4.**If a room were 2 metre longer and 3 metre broader, its area would have increased by 75 sq. m. if it were one metre shorter and 2 metre broader, the area would have increased by 16 sq. m. find the length and breadth. (3 Marks)

**5.**Solve by Elimination method $\frac{x}{2}+\frac{2y}{3}=-1\text{\hspace{0.33em}}and\text{\hspace{0.33em}}x-\frac{y}{3}=3$(3 Marks)

**6.**The sum of the digits of a two digit number is 9. Nine times this number is twice the number obtained by reversing the digits. Find the number. (3 Marks)

**7.**The ratio of the incomes of two persons is 9 : 7 and the ratio of their expenditures is 4 : 3. If each of them manages to save ₹ 2000 per month, find their monthly incomes. (3 Marks)

**8.**Ved travels 600 km to his home partly by train and partly by car. He takes 8 Hours, If he travels 120 km by train and the remaining distance by car. If he travels 200 km by train and the remaining distance by car, he takes 20 minutes longer. Find the speed of the train and the car separately. (3 Marks)

**9.**A boat goes 16 km upstream and 24 km downstream in 6 hrs. Also it covers 12 km upstream and 36 km downstream in the same time. Find the speed of the boat upstream and downstream. (3 Marks)

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