Solution: Let the sides of the two squares be x m and y m. Therefore, their perimeter will be 4x and 4y respectively And area of the squares will be ${{x}^{2}}~and~{{y}^{2}}~$ respectively. Given,...

Solution: Let us say, the average speed of passenger train =  x km/h. Average speed of express train = (x + 11) km/h Given, time taken by the express train to cover 132 km is 1 hour less than the...

Solution: Let the time taken by the smaller pipe to fill the tank = x hr. Time taken by the larger pipe = (x – 10) hr Part of tank filled by smaller pipe in 1 hour = 1/x Part of tank filled by...

Solution: Let us say, the speed of the train be x km/hr. Time taken to cover 360 km = 360/x hr. As per the question given, $\Rightarrow \left( x~+\text{ }5 \right)\left( 360-1/x \right)\text{...

Solution: Let us say, the larger and smaller number be x and y, respectively. As per the question given, ${{x}^{2~}}~{{y}^{2}}~=\text{ }180\text{ }and~{{y}^{2}}~=\text{ }8x$ $\Rightarrow...

Solution: Let us say, the shorter side of the rectangle be x m. Then, larger side of the rectangle = (x + 30) m As given, the length of the diagonal is = x + 30 m Therefore, $\Rightarrow...

Solution: Let us say, the marks of Shefali in Maths be x. Then, the marks in English will be 30 – x. As per the given question, $\left( x~+\text{ }2 \right)\left( 30\text{ }~x~\text{ }3...

Solution: Let us say, present age of Rehman is x years. Three years ago, Rehman’s age was $\left( x-3 \right)$ years. Five years after, his age will be $\left( x~+\text{ }5 \right)$ years. Given,...

Solution: $\left( i \right)~x-1/x~=\text{ }3$ $\Rightarrow ~{{x}^{2}}~\text{ }3x~-1\text{ }=\text{ }0$ On comparing the given equation with $a{{x}^{2}}~+~bx~+~c~=\text{ }0$ , we get $a~=\text{...

$\left( \mathbf{iii} \right)\text{ }\mathbf{4}{{\mathbf{x}}^{\mathbf{2}}}~+~\mathbf{4}\surd \mathbf{3x}~+\text{ }\mathbf{3}\text{ }=\text{ }\mathbf{0}$ On comparing the given equation...

$\left( \mathbf{i} \right)\text{ }\mathbf{2}{{\mathbf{x}}^{\mathbf{2}}}~~\mathbf{7x}~+\text{ }\mathbf{3}\text{ }=\text{ }\mathbf{0}$ On comparing the given equation with $a{{x}^{2}}~+~bx~+~c~=\text{...

$\left( \mathbf{iii} \right)\text{ }\mathbf{4}{{\mathbf{x}}^{\mathbf{2}}}~+\text{ }\mathbf{4}\surd \mathbf{3x}~+\text{ }\mathbf{3}\text{ }=\text{ }\mathbf{0}$ Converting the equation into...

Solutions: $\left( \mathbf{i} \right)\text{ }\mathbf{2}{{\mathbf{x}}^{\mathbf{2}}}~-\mathbf{7x}~+\text{ }\mathbf{3}\text{ }=\text{ }\mathbf{0}$ $\Rightarrow 2{{x}^{2}}~-7x~=\text{  }3$ Dividing by 2...