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
Answers
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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