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?
Answers
Answer:
The fraction of water lost by the fifth day is 31/32, the remaining fraction is 1/32 and the amount to be put to fill the tank is 9687.50 Liters.
Step-by-step explanation:
Step 1 : Calculate the amount lost in each of the five days.
Day 1 : ½ × 10000 = 5000
Day 2 : ½ × 5000 = 2500
Day 3 : ½ × 2500 = 1250
Day 4 : ½ × 1250 = 625
Day 5 : ½ × 625 = 312.50
Step 2 : Calculate the total amount of water lost.
Total = 5000 + 2500 + 1250 + 625 + 312.50 = 9687.50 Liters.
Step 3: Calculate the remaining amount of water.
10000 - 9687.50 = 312.50 Liters.
Step 3 : Answer the questions.
1) Fraction of the water lost is :
= 9687.50/10000 = 31/32
2) Fraction of the water that remains.
312.50/10000 = 1/32
3) The amount of water that needs to be put back to the tank in order to make it full.
31/32 × 10000 = 9687.50 Liters.
Answer:
Here you go your answer is above
