When three brands of juices are mixed in the ratio of 3 : 4 : 5 and 4: 5:6, the cost
price of the two piece mixtures comes out to be Rs. 20 per litre and Rs. 25 per litre
respectively. Find the cost price of a litre of mixture of juices in which the three brands
of original juices are mixed in the ratio of 6:7:8
Answers
Given : three brands of juices are mixed in the ratio of 3 : 4 : 5 and 4: 5:6, the cost price of the two mixtures comes out to be Rs. 20 per litre and Rs. 25 per litre respectively.
To Find : the cost price of a litre of mixture of juices in which the three brands of original juices are mixed in the ratio of 6:7:8
Solution:
Cost of juice per litre are A , B & C respectively
ratio of 3 : 4 : 5 then mixture Rs. 20 per litre
3 + 4 + 5 = 12 Litre
12 * 20 = 240 Rs
3A + 4B + 5C = 240 Eq1
ratio of 4 : 5 : 6 then mixture Rs. 25per litre
4 + 5 + 6 = 15 Litre
15 * 25 = 375 Rs
4A + 5B + 6C =375 Eq2
Eq2 - Eq1
=> A + B + C = 135
=> 2A + 2B + 2C = 270
4A + 5B + 6C =375
2A + 2B + 2C = 270
Adding Both
6A + 7B + 8C = 645
6 + 7 + 8 = 21
645/21 = 30.7
cost price of a litre of mixture of juices in which the three brands
of original juices are mixed in the ratio of 6:7:8 is 30.7
But Actually Data is wrong
as 3A + 4B + 5C = 240
2A + 2B + 2C = 270
=> A + 2B + 3C = - 30 ( which is not possible ) as Cost can not be negative
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