Question

Two buckets can hold 250 litres and 175 litres of water respectively. Find the maximum capacity of
the bucket that can measure the water from both the buckets exactly​

Answer 1

The maximum capacity of the bucket that can measure the water from both the buckets exactly is 75 L.

Concept used:

• For finding the maximum capacity of a container we have to find the HCF of the given numbers.

• We have use Euclid's division lemma to find the HCF.

Euclid's division lemma:

a = bq + r

Here, a = Dividend, b = divisor, q = quotient and r = remainder

Dividend = (Divisor x quotient) + Remainder

Given:

Capacities of two buckets are 250 L and 175 L.

To find:

The maximum capacity of the bucket that can measure the water from both the buckets exactly.

Solution:

Step 1: Using Euclid's division lemma in 250 L and 175 L.

Here, 250 > 175

Now, 250 = (175 x 1) + 75

Here, remainder = 75 ≠ 0.

So, new dividend is 175 and divisor is 75.

Step 2: Using Euclid's division lemma in 175 L and 75 L.

Now, 175 = (75 x 2) + 25

Here, remainder = 25 ≠ 0.

So, new dividend is 75 and divisor is 25.

Step 3: Using Euclid's division lemma in 75 L and 25 L.

Now, 75 = (25 x 3) + 0

Here, remainder is zero and divisor is 25.

So, the HCF of 250 and 175 is 25.

Hence, the maximum capacity of the required container is 25 L.

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