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Two tanks contain 100 litres and 150 litres of water respectively. Find the maximum capacity of the tank which can measure the quantity of water in either of the tanks in exact number of times.

Question

Two tanks contain 100 litres and 150 litres of water respectively. Find the maximum capacity of the tank which can measure the quantity of water in either of the tanks in exact number of times.

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Solution

The problem is asking for the maximum capacity of a tank that can measure the quantity of water in either of the two tanks an exact number of times. This is essentially asking for the greatest common divisor (GCD) of the two tank capacities.

Here are the steps to find the GCD of 100 litres and 150 litres:

  1. First, list the prime factors of each number:

    • The prime factors of 100 are 2, 2, 5, 5.
    • The prime factors of 150 are 2, 3, 5, 5.

  2. Then, identify the common prime factors:

    • The common prime factors are 2, 5, 5.

  3. Finally, multiply these common prime factors together to find the GCD:

    • 2 * 5 * 5 = 50 litres.

So, the maximum capacity of a tank that can measure the quantity of water in either of the two tanks an exact number of times is 50 litres.

This problem has been solved

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