Question

a dragon drunk 1/5 of water in a lake. after a break he drank 1/4 pf remaining water. after another break he drank 1/3 of remaing water. After another break he drrank 1/2 of remaining water.how much water is left in the lake, compared to initial amount

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Answer 1

SOLUTION

A dragon drunk 1/5 of water in a lake. after a break he drank 1/4 pf remaining water. after another break he drank 1/3 of remaining water. After another break he drunk 1/2 of remaining water.

TO DETERMINE

The amount of water is left in the lake, compared to initial amount

EVALUATION

Let initial amount of water = w

First A dragon drunk 1/5 of water in a lake

So the dragon drunk

$\displaystyle \sf{ = w \times \frac{1}{5} = \frac{w}{5} }$

Amount of Water left

$\displaystyle \sf{ = w - \frac{w}{5} = \frac{4w}{5} }$

Now A dragon drunk 1/4 of water in a lake

So the dragon drunk

$\displaystyle \sf{ = \frac{4w}{5} \times \frac{1}{4} = \frac{w}{5} }$

Amount of Water left

$\displaystyle \sf{ = \frac{4w}{5} - \frac{w}{5} = \frac{3w}{5} }$

A dragon drunk 1/3 of water in a lake

So the dragon drunk

$\displaystyle \sf{ = \frac{3w}{5} \times \frac{1}{3} = \frac{w}{5} }$

Amount of Water left

$\displaystyle \sf{ = \frac{3w}{5} - \frac{w}{5} = \frac{2w}{5} }$

A dragon drunk 1/2 of water in a lake

So the dragon drunk

$\displaystyle \sf{ = \frac{2w}{5} \times \frac{1}{2} = \frac{w}{5} }$

Amount of Water left

$\displaystyle \sf{ = \frac{2w}{5} - \frac{w}{5} = \frac{w}{5} }$

Finally the amount of water left

$\displaystyle \sf{ = \frac{w}{5} }$

$\displaystyle \sf{ = \frac{1}{5} \times Initial \: \: amount }$

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Answer 2

SOLUTION

A dragon drunk 1/5 of water in a lake. after a break he drank 1/4 pf remaining water. after another break he drank 1/3 of remaining water. After another break he drunk 1/2 of remaining water.

TO DETERMINE

The amount of water is left in the lake, compared to initial amount

EVALUATION

Let initial amount of water = w

First A dragon drunk 1/5 of water in a lake

So the dragon drunk

=w× 1/5 = w/5

Amount of Water left

=w − w/5 = 4w/5

Now A dragon drunk 1/4 of water in a lake

So the dragon drunk

= 4w/5 × 1/4 = w/5

Amount of Water left

= 4w/5 − w/5 = 3w/5

A dragon drunk 1/3 of water in a lake

So the dragon drunk

= 3w/5 × 1/3 = w/5

Amount of Water left

= 3w/5 − w/5 = 2w/5

A dragon drunk 1/2 of water in a lake

So the dragon drunk

= 2w/5 × 1/2 = w/5

Amount of Water left

= 2w/5 − w/5 = w/5

Finally the amount of water left

= w/5

= 1/5 ×Initialamount