Linear Equation...

Two numbers are in the ratio $$4 : 7$$. If thrice the larger be added to twice the smaller, the sum is $$59$$. Find the numbers.

In an examination, a student scores $$4$$ marks for every correct answer and loses $$1$$ mark for every wrong answer. If he attempts in all $$60$$ questions and secures $$130$$ marks, the number of questions he attempts correctly, is ___

Amit is now $$6$$ times as old as his son. Four years from now, the sum of their ages will be $$43$$ years. Determine Amit's present age:

If  $$\displaystyle \frac{1}{3}\left ( 7-4x \right )-\frac{1}{4}\left ( 11-5x \right )+1=x-\frac{1}{2}\left ( 3x-7 \right )$$, then $$x=$$

The ten's digit of a two digit number exceeds its unit's digit by $$4$$. If the ten's digit and the unit's digit are in the ratio $$3 : 1$$, find the number.

Solve the following equation: 

A farmer divides his herd of $$x$$ cows among his $$4$$ sons so, that first son gets-one-half of the herd, the second son get, one-fourth, the third son gets one-fifth, and the fourth son gets $$7$$ cows, then the value of $$x$$ is : 

The difference of the squares of two consecutive even natural numbers is 92. Taking x as the smaller of the two numbers, form an equation in x, and hence find the larger of the two numbers.

The difference between two numbers is $$8$$ and their ratio is $$1:5$$. Which of the following is the smaller number?

The solution of the equation 
$$\displaystyle \frac{3a-2}{3}+\frac{2a+3}{2}=a+\frac{7}{6}$$ is