A bucket holds somewhere between 100 and150 liters of water. If we fill as many as 3 liters containers we will be left with 1 liter of water, similarly is the case with 4 liters container and 5 liters container then what is the capacity of bucket
So the number must be such that
when divided by 3 , leaves a remainder of 1
when divided by 4 , leaves a remainder of 1
when divided by 5 , leaves a remainder of 1
Find the lowest common number is these sets:
4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64.....
5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 .....
6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 ...
A slow and tedious processs
but did you notice that 61 would work, but it is not between 100 and 150.
However 3x4x5 = 60, so if we add multiples of 60 we have numbers with the given property
So numbers which satisfy the original condition are:
1, 61, 121, 181 , ...
and the one that fits between 100 and 150 is
121
for a fun topic along these lines, Google and look into
the "chinese remainder theorem"
Well, it seems like the bucket is quite the elusive character! Let me do some calculations, but be warned, my math skills can sometimes be as soggy as a waterlogged clown shoe.
So, if we start with the assumption that the bucket holds x liters of water, and we can fill up the bucket with 3-liter, 4-liter, and 5-liter containers until we're left with 1 liter, we can set up some equations.
First, we know that x divided by 3, with a remainder of 1, must be an integer. Similarly, x divided by 4, with a remainder of 1, and x divided by 5, with a remainder of 1, must also be integers.
Now, let's find the common multiples of 3, 4, and 5:
Starting with 3: 3, 6, 9, 12...
Then with 4: 12, 24, 36...
And finally with 5: 15, 30, 45...
Hmmm, there's something fishy going on here. We're looking for a number that appears in all three of these lists. It seems like the clownish universe is conspiring against us, as there are no numbers that fit the bill.
So, my friend, it looks like our bucket might have magical properties that defy mathematical logic! Or perhaps I need to work on my circus math skills. Either way, it seems we're left with a mystery instead of a definitive answer.
Let's solve this step-by-step:
Step 1: Find the common multiples of 3, 4, and 5.
The multiples of 3 are: 3, 6, 9, 12, 15, 18, ...
The multiples of 4 are: 4, 8, 12, 16, 20, ...
The multiples of 5 are: 5, 10, 15, 20, 25, ...
The common multiples of 3, 4, and 5 are: 12, 15, 20, ...
Step 2: Determine the capacity of the bucket.
Since the capacity of the bucket is between 100 and 150 liters, we need to find a common multiple within this range.
12 liters: If we have 12 liters of water, we can fill four 3-liter containers, three 4-liter containers, and two 5-liter containers, leaving us with 1 liter of water. However, 12 liters is not in the given range of 100 to 150 liters.
15 liters: If we have 15 liters of water, we can fill five 3-liter containers, three 4-liter containers, and three 5-liter containers, leaving us with 1 liter of water. However, 15 liters is also not in the given range.
20 liters: If we have 20 liters of water, we can fill six 3-liter containers, five 4-liter containers, and four 5-liter containers, leaving us with 1 liter of water. Fortunately, 20 liters is within the given range of 100 to 150 liters.
Therefore, the capacity of the bucket is 20 liters.
To find the capacity of the bucket, we can use a process called reverse engineering.
Step 1: Let's assume the capacity of the bucket is x liters.
Step 2: If we fill 3 liters containers, we are left with 1 liter of water. This means that (x - 1) must be divisible by 3. In other words, (x - 1) % 3 = 0.
Step 3: Similarly, if we fill 4 liters containers, we are left with 1 liter of water. This means that (x - 1) must be divisible by 4. In other words, (x - 1) % 4 = 0.
Step 4: Lastly, if we fill 5 liters containers, we are also left with 1 liter of water. This means that (x - 1) must be divisible by 5. In other words, (x - 1) % 5 = 0.
Step 5: Let's find the common multiple between 3, 4, and 5 that satisfies all three conditions.
To do this, we can start by incrementing multiples of the largest number (5) until we find a number that satisfies the condition for the other two numbers (3 and 4) as well.
Checking the multiples of 5:
5, 10, 15, 20, 25, 30, 35...
We find that the first multiple of 5 that is also divisible by 3 and 4 is 20, which satisfies the conditions (20 % 3 = 2, 20 % 4 = 0, 20 % 5 = 0).
Step 6: Adding 1 to 20 gives us the capacity of the bucket. Therefore, the capacity of the bucket is 21 liters.
So, the capacity of the bucket is 21 liters.