Question

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.
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:

9687.5

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