Linear Equation...

A piece of string is $$80$$ cm long. It is cut into three pieces. The longest piece is $$3$$ times as long as the middle sized piece and the shortest piece is $$46$$ cm shorter than the longest piece. Find the length of the shortest piece.

The sum of one half, one third and one fourth of a number exceed the number itself by $$12$$. The number is

Rina is $$x$$ years old. Her sister Bina is $$5$$ years older than her. If their ages add up to $$15$$, then Bina's age is

When $$19$$ is subtracted from the product of $$p$$ and $$4$$, the result is $$17$$. 

The perimeter of an isosceles triangle is $$\displaystyle 3\frac { 9 }{ 4 } $$ cm. The base of an isosceles triangle is $$\dfrac{3}{2}$$ cm. What is the length of either of the remaining equal sides?

The sum of three consecutive multiples of $$9$$ is $$135$$, then the multiples are

In a division, a student took $$63$$ as divisor instead of $$36$$. His answer was $$24$$. The correct answer is -

When a number is divided by $$4$$, the result is $$-9$$. The number is 

In a contest there were $$10$$ problems. Each correct answer is eligible for $$5$$ points while each incorrect answer is penalized with a deduction of $$2$$ points. Venkat answered all the questions but got only $$29$$ points. The number of correct answers of Venkat was

In an examination, a student scores 4 marks for every correct answer and loses 1 mark for every wrong answer. If he attempts all 75 questions and secures 125 marks, the number of questions he attempted correctly, is