Linear Equations Having Two Variables and their Solutions

The sum of the two numbers is $20$ and their product is $75$. What is the sum of their reciprocals?

$12$ girls decided to contribute $₹750$ each and buy a gift for their teacher. Suddenly, a few of the girls dropped out and consequently, the rest of the girls had to pay $₹150$ more. Find the the number of girls who dropped out.

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 $2x+3y=31$ and $7x=5y$, then what is the value of $2y-x$?

If$3x+7y=75$ and $5x-5y=25$. What is the value of $x+y$?

The expression $x-3$ is read as

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 $x-y$ ?

In the following question, two equations numbered I and II are given. You have to solve both the equation and give answer.

A. If $x>y$

B. If $x\ge y$

C. If $x<y$

D. If $x\le y$

E. If $x=y$ or the relationship cannot be established.

$$\begin{gathered} \mathrm{I}. 10x+11y=19 \\ \mathrm{II}. 4x+2y=\frac{298}{55} \end{gathered}$$

The value of variable in the expression is

The number of rows is $6$ class is equal to the number of columns . If the number of rows is '$b$' then the total students in the $6$ class are:

A sum of $₹36.90$ is made of $180$ coins which are either $10$ paise coins or $25$ paise coins. The number of $10$ paise coins is:

In gradient-intercept form of equation y = mx + c, the 'c' denotes _____.

$\mathrm{X}$ is four years older than $\mathrm{Y}$, who is twice as old as $\mathrm{Z}$. If the sum of ages of $\mathrm{X}$, $\mathrm{Y}$ and $\mathrm{Z}$ is $34$ years, how old is $\mathrm{X}$?

The price of potatoes is $₹x/\mathrm{kg}$ and price of onion is $₹10$ more than the price of potatoes. Therefore the price of onion is?

On children's day sweets were to be equally distributed among $175$ students in a school. Actually on the day $35$ children were absent and therefore each child got $4$ sweets extra. How many sweets were available in all for distribution?

The sum of the present ages of father and son is $80 \mathrm{years}$. $4 \mathrm{years}$ ago, the ratio of their age was $2:1$. Father's present age will be-