Question

A chocolates box is in the shape of a square. Each chocolate takes 1 square cm of area. Another box of chocolates which is in the shape of square has 211 more chocolates than the first box. Find out the number of chocolates in the first box.

• A. 105cm
• B. 106 cm
• C. 108 cm
• D. None of these

Answer 1

The correct option is A

105cm

Let the side of first square be x
So, Total area of first square box = $x^2$
Let the side of second square = y
Its area = $y^2$
Since, second box has 211 more number of chocolates that means
Difference in the areas of first and second square box =211
$y^2-x^2$ = 211
Since, 211 is a prime number it has two factor 211 and 1
(y-x)(y+x) = 211
(106-105)(106 +105) = 211
So, side of first square box = 105cm
Side of second square box = 106 cm