Two jars, J1 and J2, contain 120 ml and 80 ml of a honey and water mixture, respectively.
J1 has honey and water in the ratio 3:1.
J2 has honey and water in the ratio 1:3.
A quantity of the mixture is transferred from J₁ to J₂. After the transfer, the ratio of honey to water in J₂ becomes 1:1. What is the volume of the mixture (in ml) transferred from J1 to J2?
Show answer & explanation
Correct answer: C
Explanation
J₁ = 120 ml, Honey : Water = 3 : 1
J₂ = 80 ml, Honey : Water = 1 : 3
Ratio in J₂ after transfer = 1 : 1
In J₁:
Honey = 120 × 3/4 = 90 ml
Water = 120 × 1/4 = 30 ml
In J₂:
Honey = 80 × 1/4 = 20 ml
Water = 80 × 3/4 = 60 ml
Let's assume x ml of the mixture was transferred from J₁ to J₂.
In the transferred mixture:
Honey = 3x/4
Water = x/4
New amount of honey in J₂ = 20 + 3x/4
New amount of water in J₂ = 60 + x/4
Ratio = 1 : 1
20 + 3x/4 = 60 + x/4
3x/4 − x/4 = 60 − 20
x/2 = 40
x = 80 ml