Question

Everyday a factory making pencils sends $2077$ pencils to the town market and $3701$ pencils to market in other states .It was found little more than 614 pencils remained in the factory. If it is known that the factory makes a perfect number of pencils every day . What is the smallest number of pencils remaining in the factory?

Answer 1

Hint:In this question, at first suppose the smallest number of pencils , after that try to find out the nearest perfect number which is equal to the total number of pencils and last calculate it to find the smallest number of pencils.

Complete step-by-step answer:
Let us suppose that the smallest number of pencils remaining in the factory is x .
Number of remaining pencils in the factory is $614$.
So that the number of pencils remaining in the factory will be $$$$$614+x$.
Now total number of pencils manufactured every day in factory
                                       = $2077pencils+3701pencils+(614+x)remaining\,pencils$
                                        =$2077+3701+(614+x)$
                                        =$6392+x …………………………..(i)$
As it is given, the factory makes a perfect number of pencils every day .
Therefore nearest perfect square of $6392$ is $6400$
Now it is clear that the factory makes 6400 pencils every day.
By equation (i)
     $6400=6392+x$
            $x=6400-6392$
            $x=8$
Hence number of remaining pencils in factory=$614+8=622$

Additional Information:Perfect square- A perfect square is a number that can be expressed as the product of two equal number numbers.
Examples: $1,4,9,100,144$

Note:In such type of questions, the concept of nearest should be cleared, otherwise it will be difficult to find the nearest perfect square. Nearest number is a part of rounded number .Example $341$ rounded to the nearest hundred is $300$.