Question

If a large marble box has $65$ rows and $45$ columns of marble containers, the number of marbles the box can contain is .

• A. $2625$
• B. $2725$
• C. $2825$
• D. $2925$

Answer 1

The correct option is D $2925$

As per the question, the marble box has $65$ rows and $45$ columns of marble containers.

$\therefore$ Total number of possible marbles in the box= Total number of marble containers= $65\times 45$

$65\times 45$ denotes the multiplication of two 2-digits number by a $2$-digit number, which can be solved using box method.

$65\times 45$ can also be written as $(60+5)\times (40+5)$.

Now, placing the expanded numbers on box as shown in below figure,



Now, multiplying numbers on top of box by number on left of box as shown in below figure,


Simplifying the numbers inside the boxes as shown in below figure,


Now, sum of numbers in all the boxes will give the result,
$\therefore 45\times 65=2,400+300+200+25=2,925$ as shown in below figure,
$\therefore$ The marble box, which has $65$ rows and $45$ columns, can contain $2,925$ number of marbles.