Applications of Linear Equations

If the height of a triangle whose area is $36 \mathrm{sq} \mathrm{m}$ and the length of its base is $12 \mathrm{m}$  is $x \mathrm{m}$, then find the value of $x$.

Twice a number is as much greater than $30$ as the three times of the number less than $60$. The number is

If two angles are complementary and one angle is $10°$ greater than the other, and the smaller angle of the two is $x°$ then find $x$.

When$9$ is added to two times a number, we get $67$. The number is

The difference between two whole numbers is $66$. The ratio of the two numbers is $2:5$. Then the sum of those two numbers is

The perimeter of the rectangle is $20 \mathrm{cm}$. If the length of the rectangle is $6 \mathrm{cm}$, and its breadth is $x \mathrm{cm}$ then find $x$.

When I triple a certain number and add $2,$I get the same answer as I do when I subtract the number from $50$. Find the number.

One number is half of the other. Sum of these two numbers is equal to $6$. Then the two numbers are

The sum of digits of a two-digit number is $17$. On reversing its digits, the new number is $9$ more than the original number. Find the number.

The organisers of an essay competition decide that a winner in the competition gets a prize of $₹500$ and a participant, who does not win, gets a prize of $₹100$. The total prize money distributed is $₹4800$. Find the number of winners, if the total number of participants is $36$.

Two men and three boys can complete a work in 5 days. Four men and four boys can complete the same work 3, days. How many days will one man alone complete the same amount of work.

The sum of a two digit number and the number obtained by reversing the digit is $165$. Also the difference of these numbers is $9$. find the numbers.

If $1$, is added to the denominator of a fraction the fraction becomes $\frac{1}{2}$, if $1$ is added to the numerator of the fraction. the fraction becomes $1$, find the fraction. 

The sum of numerator and denominator of a fraction is$12$. if the denominator is increased by $3$, the fraction becomes $\frac{1}{2}$. find the fraction.

The ratio of two numbers is $\frac{2}{5}$. If $4$ is added in first and $32$ is subtracted from the second the ratio becomes the reciprocal of the original ratio. find the numbers.

Seven more than a two- digit number is equal to two less than the number obtained by reversing the digits the sum of the digits is $5$, find the number.

The sum of a two-digit number and the number obtained by reversing the digits is $110$and the difference of two digits is  $2$ find the number.

In a two-digit number, the sum of the digits is $7$. the difference of the number obtained by reversing the digits and the number itself is $9$. find the number.

The sum of four times the first number and three times the second number is $15$. the difference of three times the first number and twice the second number is$7$. find the numbers. 

The length of a rectangle is twice its width. if its perimeter is 30untis,find its dimensions.