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. 

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Answer 1

Given :-

• Arjun used half of his total number number of arrows to cut down arrows thrown by Bheeshm.
• He used 6 more arrows to kill the rath driver of Bheeshm.
• Again, with one arrow each he knocked down the rath, flag & bow of Bheeshm.
• At last, with one more than four times the square root of arrows he knocked down Bheeshm.

To Find :-

• Total number of arrows Arjun had.

Solution :-

Suppose the total number of arrows Arjun had be x.

A.T.Q,

• Number of arrows used to cut down arrows of Bheeshm = x/2
• Number of arrows used to kill the rath driver = 6
• Number of arrows used to knock down flag, rath and bow of Bheeshm = 1 each (total 3)
• Remaining number of arrows = 4√x + 1

By hypothesis, we have,

⇒ x/2 + 6 + 3 + 4√x + 1 = x

⇒ x + 20 + 8√x = 2x

⇒ x = 20 + 8√x .......(1)

Putting x = y², in (1), we get,

⇒ y² = 20 + 8y

⇒ y² - 8y - 20 = 0

By splitting the middle term, we get,

⇒ y² - 10y + 2y - 20 = 0

⇒ (y - 10)(y + 2) = 0

⇒ y = 10 or y = -2

Neglecting negative value, we get,

⇒ y = 10

⇒ x = y² ⇒ x = (10)² = 100

Hence, the number of arrows which Arjun had = 100.

[NOTE: x was taken as y² in order to form a quadratic equation.]