Question

The angry Arjun carried some arrows for fighting with Bheeshm. With half the arrows, he cut down the arrows thrown by Bheeshm on him. Six arrows, he used to kill the rath driver of Bheeshm. With one arrow each he knocked down respectively the rath, flag and the bow of Bheeshm. Finally, with one more than four times the square root of arrows he laid Bheeshm unconscious on an arrow bed. Find the total number of arrows Arjun had.

• A. $100$
• B. $200$
• C. $150$
• D. $80$

Answer 1

Answer: (A)

$100$

Let the total number of arrows carried by Arjun be $x$

Number of arrows used to cut down the arrows thrown by Bheeshm $=\frac{x}{2}$

Number of arrows used to kill the rath driver of Bheeshm $=6$

Number of arrows used to knock down the rath, flag and the bow of Bheeshm $=3$

Number of arrows left $=x-(\frac{x}{2}+6+3)=\frac{x}{2}-9$

Remaining arrows were used to kill Bheeshm.

So, Number of arrows used to kill Bheeshm $=\frac{x}{2}-9$

Also, it is given that

Number of arrows used to kill Bheeshm $=1+4\sqrt{x}$

$\therefore 1+4\sqrt{x}=\frac{x}{2}-9$

$\therefore 4\sqrt{x}=\frac{x}{2}-10$

$\therefore 16x=\frac{x^2}{4}+100-10x$

$\therefore x^2-104x+400=0$

$\therefore (x-100)(x-4)=0$

$\therefore x=100$ or $x=4$

Arjun used $6$ arrows to kill rath driver of Bheeshm

$x=4$ cannot be answer

So, total number of arrows $=100$