Question

you have a ceramic jar of hair oil containing 44% of almond oil you decide to replace a part of this hair oil with another hair oil containing 20% of almond oil what fraction of the hair oil did you replace if the hair oil now contains 24% of amount on it​

Answer 1

5/6 of fraction of the hair oil  containing 44% of almond oil  is replaced by another hair oil containing 20% of almond oil so that hair oil now contains 24% of almond oil.

Given:

• A ceramic jar of hair oil containing 44% of almond oil
• Replaced a part of this hair oil with another hair oil containing 20% of almond oil
• Hair oil now contains 24% of almond oil

To Find:

• Fraction of the hair oil replaced

Solution:

Step 1:

Assume that Initial hair oil in  ceramic jar is 100x   litre

Almond oil = (44/100)100x = 44x  litre

Step 2:

Assume that 100y litre is replaced

Then Almond oil removed = (44/100)100y = 44y  litre

Step 3:

Almond oil in another = (20/100)100y = 20y  litre

Step 4:

Hence Almond oil now = 44x  - 44y  + 20y

= 44x  - 24y   litre

Step 5:

Now Almond oil = (24/100)100x = 24x  litre

Step 6:

Equate Both

44x  - 24y = 24x

=> 20x  = 24y

=> y/x  = 20/24

=> y/x  = 5/6

=> 100y/100x  = 5/6

5/6 of fraction of the hair oil  is replaced