Two metals X and Y are to be used for making two different alloys. If the ratio by weight of X : Y in the first alloy is 6 : 5 and that in the second is 7 : 13, how many kg of X metal must be melted along with 11 kg of the first alloy and 20 kg of the second so as to produce a new alloy containing 40% of metal Y?
Answers
14 kg of X metal must be melted along with 11 kg of the first alloy and 20 kg of the second so as to produce a new alloy containing 40% of metal Y
Step-by-step explanation:
ratio by weight of X : Y in the first alloy is 6 : 5 and that in the second is 7 : 13
First Alloy = 11 kg
X metal = (6/11)*11 = 6 kg
Y metal = (5/11)* 11 = 5 kg
Second Alloy = 20 kg
X metal = (7/20)*20 = 7 kg
Y metal = (13/20)* 20 = 13 kg
Let say K kg of X metal added
Then Total X metal = 6 + 7 + K = 13 + K kg
Y metal = 5 + 13 = 18 kg
Total = 11 + 20 + K = 31 + K kg
containing 40% of metal Y
=> (18/(31 + K) ) * 100 = 40
=> 180 = 124 + 4K
=> 4K = 56
=> K = 14
14 kg of X metal must be melted along with 11 kg of the first alloy and 20 kg of the second so as to produce a new alloy containing 40% of metal Y
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