Solving Linear Equations in One Variable

If $₹1260$ is divided into three parts such that one-third of the first part, one-fourth of the second part, and one-fifth of the third part are equal, then find the smallest part of the money.

Solve:

$\frac{4\left(3x-2\right)+2\left(1-x\right)}{3\left(x-1\right)+5\left(2x-3\right)}=\frac{7}{4}$

$\frac{17(2-x)}{1-7x}+\frac{5(x+12)}{7x-1}=8$

Solve for x.

A woman sells to the first customer half her stock of apples and half an apple, to the second customer she sells half her remaining stock and half an apple, and so on to the third and to the fourth customer. She finds that she has now 15 apples left. How many apples did she have before she started selling?

If $\frac{3x}{\left(x-a\right)\left(x-b\right)}=\frac{2}{x-a}+\frac{1}{x-b}$ then, $a:b=?$

The number of boys in a school was $30$ more than the number of girls(not equal to $0$). Subsequently, a few more girls joined the same school. Consequently, the ratio of boys and girls became $3:5$. Find the minimum number of girls who joined subsequently.

Solve: 

$\frac{x}{3}+1=\frac{7}{15}$

Here is a calendar. Ask your friend to choose a$3\times 3$  square in this and tell you the smallest number in that square. In your mind, add $8$ to that number and multiply it by $9$. Give him/her this answer as the sum of the number in his/her square. He/She will be surprised by how you did it. Can you explain how you can work out this problem by forming an equation and solving it.

For the given geometrical figure, find $x$.

For the given geometrical figure, find $x$.