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In a bowl containing 60 ml orange juice, 40 ml of water is poured. Thereafter, 100 ml of apple juice is poured to make a fruit punch. Madhu drinks 50 ml of this fruit punch and comments that the proportion of orange juice needs to be higher for better taste. How much orange juice should be poured into the fruit punch that remained, in order to bring up the level of orange juice to 50 percentage?
Initially, there is 60 ml orange juice, now 40 ml water is poured into it and again 100 ml apple juice is mixed into it :
Hence first jar has : Apple - 100 ml
Water - 40 ml ( i.e they are in the ratio of 5:2:3 for apple:water:orange )
Orange - 60 ml
Now as 50 ml of mixture is consumed , the 50 ml consumed juice composition should be 5:2:3 for apple : water : orange , this implies :
consumed has : Apple - 25 ml , water - 10 ml, orange - 15ml.
Therefore, the remaining part is :
Apple :100-25 = 75 ml , Water: 40-10 = 30ml, Orange: 60-15 = 45ml.
Now, lets assume we are adding X ml of orange to this remaining left out mixture to make it 50% :
$$\ \dfrac{\ 45+X}{75+30+45+X}=\dfrac{\ 1}{2}$$
This gives X = 60 ml.
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