The two mixtures are called "P" and "Q." Only oil and diesel are contained in each of them. There are 500 liters of mixture "Q" in total. Determine how much oil is in mixture "P."

Statement I: Oil and diesel are present in "Mixture P" in a ratio of 3:2. There are 300 liters more oil in mixture "Q" than there is diesel in it, and there are 240 liters more oil than diesel in mixture "P." 

Statement II: There is a 25% excess of mixture 'Q' over mixture 'P'. There are 160 liters of diesel in mixture 'P'.

Statement III: There is a multiple of 5 in the quantity of mixture "P."

Statement IV: The amount of diesel in mixture "P" would have made up 52% of the total amount of mixture "Q" if there had been 100 liters more of it.

Solution

ATQ, Statement I: Total quantity of mixture ‘Q’ = 500 litres Quantity of oil in mixture ‘Q’ = (500 + 300)/2 = 400 litres Therefore, quantity of diesel in mixture ‘P’ = 400 – 240 = 160 litres Quantity of oil in mixture ‘P’ = 160 × (3/2) = 240 litres Therefore, statement I alone is sufficient to answer the question Statement II: Total quantity of mixture ‘P’ = 500/1.25 = 400 litres Quantity of oil in mixture ‘P’ = 400 – 160 = 240 litres Therefore, statement II alone is sufficient to answer the question. Statement III: The quantity of mixture ‘P’ is a multiple of 5. Therefore, data in statement III alone is not sufficient to answer the question. Statement IV: If the quantity of diesel in the mixture ‘P’ had been 100 litres more, then it would have been 52% of total quantity of the mixture ‘Q’ Therefore, desired quantity of diesel in mixture ‘P’ = 0.52 × 500 – 100 = 160 litres Therefore, data in statement IV alone is not sufficient to answer the question. Therefore, data in statement I and II alone is sufficient to answer the question while data in statement III and IV alone is not sufficient to answer the question.