Question

Q4. A tank contains 10,000 litres of water when full. It begins to leak. After the first day, half of
*the water is lost. After the second day, half of the remainder is lost. After the third day, half of
the remainder from the second day is lost. This continues, losing half of the remainder from
the previous day. At the end of 5 days, the leak is discovered.
KERETA in naty
a) What fraction of the water has been lost?
b) What fraction of the water remains?
c) How much water has to be put back into the tank in order to fill it up?​

Answer 1

Answer:

31/32

1/32

9687.5 litre

Step-by-step explanation:

A tank contains 10,000 litres of water

After 1st day water Leaked = 10000/2 = 5000 litre

Water remained in Tank = 10000 - 5000 = 5000 litre

After 2nd  day water Left = 5000/2 = 2500 Litre

After 3rd day water Left = 2500/2 = 1250 litre

After 4th day water Left = 1250/2 = 625 litre

After 5th day water Left = 625/2 = 312.5 litre  = 10000/32

Water Lost = 10000 - 10000/32 =  (31/32) * 10000

Fraction of water Lost = 31/32

Fraction of water remains = 1 - Fraction of water Lost

Fraction of water remains = 1 - 31/32  = 1/32

water has to be put back into the tank in order to fill it up = Water Lost = (31/32) * 10000 = 9687.5 Litre

Answer 2

Answer:

a) 96.875/100

b) 3.125/100

c) 9687.5 L

Step-by-step explanation:

At Initial stage the Tank has 10,000 L of water.

Let a = 10,000

After each day, the water almost is exactly half of the previous one.

Hence, Let r = 1/2

After 5 days, the remaining water can be found by formula of Geometric Progression (GP)

Formula : Tn = ar⁽ⁿ⁻¹⁾

Therefore, for at the end of 5th Day i.e. T₆

T₆ = ar⁽⁶⁻¹⁾

    = 10000 x 1/2⁵

    = 10000/32

    = 312.5

So after 5th day the remaining will be 312.5 L

a) Fraction of water lost = (a - T₆)/ a

                                          = (10000 - 312.5)/10000

                                          = 9687.5/10000

                                          = 96.875/100

Therefore 96.875/100 fraction of water was lost.

b) Fraction of water remaining = T₆/a

                                                     = 312.5/10000

                                                     = 0.03125

                                                     = 3.125/100

Therefore 3.125/100 fraction of water remains.

c) Water to put in order to fill the tank = a - T₆

                                                                  = 10000 - 312.5

                                                                 = 9687.5

Therefore 9687.5 L of water should be put in orer to fill the tank completely.