A jar contains a mixture of orange juice and water in the ratio of 3:1. 70 litres of the mixture were taken out, and 20 litres of water were added to it. If the water was 30% in the resultant mixture, what was the initial quantity of the mixture in the jar?
Show answer & explanation
Correct answer: C
Explanation
Given:
Orange juice : Water = 3 : 1
Mixture drawn = 70 liters
Water added = 20 liters
Water in final mixture = 30%
Formula:
Each ingredient is added to the mixture in the same proportion.
Let initial mixture = x liters
Initial water = x/4
Water drawn after 70 liters of mixture = (1/4) × 70 = 17.5
Remaining water = x/4 − 17.5
New water after adding 20 liters of water = x/4 − 17.5 + 20 = x/4 + 2.5
New total mixture = x − 70 + 20 = x − 50
Water = 30%
x/4 + 2.5 = 0.30(x − 50)
x/4 + 2.5 = 0.30x − 15
x/4 − 0.30x = −17.5
(0.25 − 0.30)x = −17.5
−0.05x = −17.5
x = 350
350 liters