Question

Two cans contain 60 and 165 litres of milk. Find a tin of maximum capacity which can measure the milk
in the two cans integral number of times,

with explanation​

Answer 1

Answer:

15 litres

Step-by-step explanation:

hcf of 60 and 165 is 15 .

Answer 2

Step-by-step explanation:

Given:-

Two cans contain 60 and 165 litres of milk.

To find:-

Find a tin of maximum capacity which can measure the milk in the two cans integral number of times?

Solution:-

Given that

Amount of milk in the two cans are 60 litres and 165 litres

To find the maximum capacity of a can which can measure the milk in two cans integral number of times we have to find the HCF of the two cans

Finding HCF of two cans of 60 litres and 165 litres of milk:-

Method-1:-

60 = 2×2×3×5

165 = 3×5×11

HCF of 60 and 165 = 3×5 = 15

Method-2:-

Euclid's Division Lemma:-

For two integers a and b there exist two integers q and r satisfying a = bq+r,0≤r<b

Consider a = 165 and b=60

=> 165 = 60×2 +45

Again a = 60 and b = 45

60 = 45×1+15

again a = 45 and b=15

45=15×3+0

HCF = 15

So 15 litres of can measures 60 litres and 165 litres of milk integral times( 5 times and 11 times respectively)

Answer:-

The maximum capacity of a can which can measure the milk in two cans integral number of times is 15 litres of can.

Used formula:-

Euclid's Division Lemma:-

For two integers a and b there exist two integers q and r satisfying a = bq+r,0≤r<b