Question

In a bangle shop, if the shopkeeper displays the bangles in the form of a square then he is left with 38 bangles with him. If he wanted to increase the size of square by one unit each side of the square he found that 25 bangles fall short of In completing the square. The actual number of bangles which he had with him in the shop was ________.

• A. 1690
• B. 999
• C. 538
• D. can't be determined

Answer 1

The correct option is B 999

Let the length of the side of the square initially be $l$.

Number of bangles it can store is $l^2$

The total number of bangles will be $l^2+38$

In the second case,

The length of the side of the square is $l+1$

The number of bangles it can now store is $(l+1{)}^2$

Now the total number of bangles equals to $(l+1{)}^2-25$

$\therefore$ $(l+1{)}^2-25$=$l^2+38$

$\Rightarrow$ $l^2+2l+1-25=l^2+38$

$\Rightarrow$ $2l=62$

$\Rightarrow$ $l=31$

$\therefore$ The total number of bangles=$(l+1{)}^2-25$=$999$

$\therefore$ Option B is correct