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 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 lost from the previous day. At the end of 5 days the leak is discovered. What fraction of water has been lost? What fraction of the water remains? How much water has to be put back into the tank in order to fill it up?
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Step-by-step explanation:
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
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