Question

A tin a mixture of two liquids a and b in the proportion 4 : 1. if 45 litres of the mixture is replaced by 45 litres of liquid b, then the ratio of the two liquids becomes 2 : 5. how much of the liquid b was there in the tin? what quantity does the tin hold?

Answer 1

Let the Mixtures of the Liquid 'a' and 'b' in a tin be 4x and x respectively.

Now, 45 liter of the Liquid 'a' is replaced by the 45 liter of the liquid 'b'. 
∴ Ratio of the liquid 'a' and 'b' = (4x - 45)/(x + 45)

According to the Question,
 (4x - 45)/(x + 45) = 2/5
 5(4x - 45) = 2(x + 45)
 20x - 225 = 2x + 90
 20x - 2x = 225 + 90
 18x = 315
  x = 17.5 

∴ Volume of the liquid a = 4x = 4(17.5) 
 = 70 liter.
Also, Volume of the liquid b = x = 17.5 liter.

Now, Total Quantity of both the liquid inn the tin = 4x + x
 = 5x
 = 5 × 17.5
 = 87.5 liter.


Hence, the total amount of the liquids hold by the tine is 87.5 liter.


Hope it helps.