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Q:

In a mixture of three varities of oils , the ratio of their weight is 4 : 5 : 8. If 5 kg of oils of the first variety, 10 kg of the second variety and some quantity of oils of the third variety are added to the mixture, the ratio of the weights of three varieties of oils becomes as 5 : 7 : 9 in the final mixture, find the quantity of third variety of oil was ? 

A) 15 kg B) 25 kg
C) 35 kg D) 45 kg

Answer:   D) 45 kg



Explanation:

Let the ratio of initial quantity of oils be 'x' => 4x, 5x & 8x.
Let k be the quantity of third variety of oil in the final mixture.
Let the ratio of initial quantity of oils be 'y'
From given details,
4x + 5 = 5y ..... (1)
5x + 10 = 7y .....(2)
8x + k = 9y ......(3)

By solving (1) & (2), we get
x = 5 & y = 5

From (3) => k = 5

Therefore, quantity of third variety of oil was 9y = 9(5) = 45kg.

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