(a)
Two types of alloys possess gold and silver in the ratio
7:22 and 21 : 37. In what ratio should these alloys be
mixed so as to have a new alloy in which gold and silver
would exist in the ratio 25: 62 ?
Answers
Given : Two types of alloys possess gold and silver in the ratio 7:22 and 21 : 37.
To Find : In what ratio should these alloys be mixed so as to have a new alloy in which gold and silver would exist in the ratio 25: 62
Solution:
Alloy 1 - Gold : Silver = 7 : 22
Alloy 2 - Gold : Silver = 21 : 37
Let say mixed in ratio m : n
Gold = (7/29)m , Silver = (22/29)m
Gold = (21/58)m , Silver = (37/58)m
Gold = 7m/29 + 21n/58 = (14m + 21n)/58
Silver = 22m/29 + 37n/58 = (44m + 37n)/58
gold and silver would exist in the ratio 25: 62
=> (14m + 21n)/(44m + 37n) = 25/62
=> (14m + 21n)62 = (44m + 37n) 25
=> 868m + 1302n = 1100m + 925n
=> 377n = 232m
=> m : n = 377 : 232
=> m : n = 13 : 8
13:8 is the ratio in which alloys be mixed so as to have a new alloy in which gold and silver would exist in the ratio 25: 62
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