Jitender Gupta and Divya Malik Solutions for Exercise 4: CHAPTER EXERCISE

Solve the following quadratic equation for $x$.

$9x^2-9\left(a+b\right)x+2a^2+5ab+2b^2=0$.

Solve  $\frac{1}{a+b+x}=\frac{1}{a}+\frac{1}{b}+\frac{1}{x}, a+b\ne 0$.

$\mathrm{A}$ takes $6$ days less than the time taken by $\mathrm{B}$ to finish a work. If both can finish the work in $4$ days, then find the time taken by $\mathrm{B}$ to finish the work.

A boat can cover $10 \mathrm{km}$ up the stream and $5 \mathrm{km}$ down the stream in $6 \mathrm{hours}$. If the speed of the stream is $1.5 \mathrm{km}/\mathrm{h}$, find the speed of the boat in still water.

A trader buys $x$ articles for a total cost of $₹600$. Write down the cost of one article in terms of $x$. If the cost per article were$₹5$ more, the number of articles that can be bought for $₹600$ would be four less. Write down the equation in $x$ for the above situation and solve it to find $x$..

In an auditorium, seats are arranged in rows and columns. The number of rows was equal to the number of seats in each row. When the number of rows was doubled and the number of seats in each row was reduced by $10$, the total number of seats increased by $300$. Find the number of rows in the original arrangement.

In an auditorium, seats are arranged in rows and columns. The number of rows was equal to the number of seats in each row. When the number of rows was doubled and the number of seats in each row was reduced by $30$, the total number of seats increased by $300$. Find the number of seats in the auditorium after re-arrangement.

The length of the sides forming right angles of a right angled triangle are $5x \mathrm{cm} \& \left(3\mathrm{x}-1\right) \mathrm{cm}$. If the area of the triangle is $60 {\mathrm{cm}}^2$, then find its hypotenuse.(in cms)