Solution of Simultaneous Equations

If the product of two numbers is $320$ and their ratio is $1 : 5$, what is the difference between the squares of these two numbers?

There are $40$ coins in a bag, consisting of $\mathrm{Rs}.5$ and $\mathrm{Rs}.2$ coins. If the total amount is $\mathrm{Rs}.140$, how many $\mathrm{Rs}.2$ and $\mathrm{Rs}.5$ coins are there in the bag?

If the graphs of the equations $y = x$ and $y = x + 3$ are drawn, then they will be _____ to one another.

$A, B, C$and $D$ purchase a gift worth $₹60$. A pays $\frac{1}{2}$ of what others are paying $B$ pays $\frac{1}{3}rd$ of what others are paying and $C$ pays $\frac{1}{4}th$ of what others are paying. What is the amount paid by $D$?

A number consists of two digits whose sum is $11$. If $27$ is added to the number, then the digits change their places. What is the number?

The sum of six consecutive even numbers of Set $A$ is $402$. What is the sum of four consecutive numbers from another Set $B$ whose lowest number is $15$ less than double the lowest number of Set $A$?

Raman's present age is three times his daughter's and nine-thirteenth of his mother's present age. The sum of the present ages of all three of them is $125$ years. What is the difference between the present ages of Raman's daughter and Raman's mother?

If $3x-5y=5$ and $\frac{x}{x+y}=\frac{5}{7}$, then what is the value of $x-y$ ?

For which value of k will the following pair of linear equations have no solution?
$3x + y = 1$,

$(2k -1)x + (k -1)y = 2k + 1$

Two bus tickets from city $A$ to $B$ and three tickets from city $A$ to $C$ cost  $₹77$ but three tickets from city $A$to $B$  and two tickets from city $A$  to $C$ cost $₹ 73$. What are the fares for cities $B$ and $C$ from $A$ ?

If $\frac{3}{x+y}+\frac{2}{x-y}=2$ and $\frac{9}{x+y}-\frac{4}{x-y}=1$, then what is the value of $\frac{x}{y}$?

Write the new equation formed by doing the given operation:

Write whether the given statement is true or false:

The value of $x$ in equation $\frac{9x}{x+5}=4$ is $4$.

Write the new equation formed by doing the given operation:

Solve the rational equation given in one variable:

$\frac{3\left(x-3\right)}{x+4}=2$

Find the equation we get on subtracting $4x$ from both the sides of equation $17x-8=22$.

The equation of $y$-axis is:

If ${72}^x·{48}^y=6^{xy},$ where $x$ and $y$ are nonzero rational numbers, then $x+y$ equals

Rajat travelled to Lucknow from Delhi. He travelled to Lucknow via train and came back via bus. The average speed of the entire journey is $\frac{200}{3} \mathrm{km}/\mathrm{hour}$ . It took him $8 \mathrm{hours}$more to reach Delhi than to reach Lucknow. Find the speed of train if the distance between Delhi and Lucknow is $800 \mathrm{km} :$

The distance between two stations is $300 \mathrm{km}$. Two trains start simultaneously from these stations and move towards each other. The speed of one of them is $7 \mathrm{km}/\mathrm{h}$ more than that of the other. If the distance between them after $2$ hours of their start is $34 \mathrm{km}$, find the speed of each train.