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Question

Two varieties of oil are mixed in the ratio 4:3 to produce the first quality and if they are mixed in the ratio 2:3, the second quality is obtained. How many kg of the first quality be mixed with 10kg of the second quality so that a third quality having the two varieties in the ratio 5:4 may be produced ?


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Solution

Let the common ratio of the first quality oil be x.

Given, the ratio is 4:3

Therefore, the total quantity of the first quality oil =4x+3x=7x

Total quantity of the second quality oil =10kg

Ratio of second quality oil is 2:3

The quantity of first oil variety =25×10=4kg

The quantity of second oil variety =35×10=6kg

The third ratio is got by mixing the first quality and 10kg of second quality.

So,

4x+43x+6=5444x+4=53x+616x+16=15x+30x=30-14x=14

Therefore, the total quantity of first quality oil =7xkg

=7×14kg=98kg

Hence, 98kg of the first quality should be mixed to get the required result.


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