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Twenty men, women and children earn twenty coins between them. Each man earns 3 coins, each woman 1.5 coins and each child 0.5 coin.
How many men, women and children are there?
Find number of each of them here!
What was the question?
Let's suppose there are m men, w women and c children.
As per given data,
m + w + c = 20 ......(1)
3m + 1.5w + 0.5c = 20 .....(2)
Multiply equation (1) by 3 and then subtracting from (2), we get,
5m + 2w = 20.
For m and w to be whole numbers, m must be 2 and w must be 5 satisfying above equation.
Hence, from (1),
c = 20 - 2 - 5 = 13.
To conclude, there are 2 men, 5 women and 13 children.
A large fresh water reservoir has two types of drainage system: small pipes and large pipes.
6 large pipes, on their own, can drain the reservoir in 12 hours.
3 large pipes and 9 small pipes, at the same time, can drain the reservoir in 8 hours.
How long will 5 small pipes, on their own, take to drain the reservoir?
Find here the exact time required!
Here is the question!
Let T be the capacity of the tank. Let L be the large pipe and S be the small pipe.
T/6L = 12
L = T/72
T/(3L + 9S) = 8
Putting L = T/72,
S = T/108
Hence T/5S = 108/5 gives S = 21.6 hours.
To conclude, small pipes require 21.6 hours i.e. 21 hours and 36 minutes to drain the reservoir.
