Question

75 litre kerosene & 25 litre petrol to be kept in tins so that they are not mixed. At least how many tins required

Answer 1

Answer:

At least 4 tins required so that they are not mixed.

Step-by-step explanation:

Given:

• 75 litre kerosene & 25 litre petrol to be kept in tins, so that they are not mixed.

To find:

• At least how many tins required.

Solution:

To find the least number of tins required, we first need to find the capacity of the tin.

• Capacity of tin = H.C.F of 75 and 25

By prime factorization method,

• Factors of 75 = 5 × 5
• Factors of 75 = 3 × 5 × 5
• Common Factors = 5 × 5

Therefore, H.C.F = 25

Thus, Capacity of tin = 25 litres

Now, finally we will find least number of tins required so that the liquids are not mixed.

• Least number of tins required for kerosene = Capacity of kerosene/Capacity of tin
• Least number of tins required for kerosene = 75/25
• Least number of tins required for kerosene = 15/5
• Least number of tins required for kerosene = 3

Then,

• Least number of tins required for petrol = Capacity of petrol/Capacity of tin
• Least number of tins required for petrol = 25/25
• Least number of tins required for petrol = 1

Therefore, total number of tins required = 3 + 1 = 4 tins

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Answer 2

Given:-

• Amount of kerosene=75 litres
• Amount of petrol=25 litres

Solution:-

$\tt \pink{Step:1}$Capicity of tin:

Let the capicity of tin be x litre

_______________

The two oil should not be mixed in any tin,so 75&25 should be divisible by x.In this way all tins will be completely filled and the two oil will not mix up..

The number of tin must he least,

So x must be as large as possible

Therefore x is the largest number which divides both 75&25 which is exactly the defination of HCF.

Hence,

x=HCF(25,75)

or x=25 litres

___________________

$\tt \pink{Step:2}$Number of tins:

Now we know that capicity of tin=25 litres

So,No of tin required for kerosene=Quantity of kerosene/capacity of tin

=75 litre/25 litre

=3 tins...

_______________

$\tt \pink{Step:3}$No of tins required for petrol

=Quantity of petrol/capacity of tin

=25 litres/25 litres

=1 tin

So,Total number of tin required=3+1=4 tins..