1. An alloy A is formed by mixing gold and silver in the ratio 2:
1. Another alloy B is formed by mixing silver and platinum
in the ratio 3 : 4. An alloy C is obtained by mixing alloys A
and B in a certain ratio such that the ratio of gold and
platinum in alloy C is 5: 6. Which of the following correctly
represents the share of silver in alloy C.
A. 29/51 B. 37/13 C. 17/31 D. 49/131 E. 19/35
Given : An alloy A is formed by mixing gold and silver in the ratio 2 : 1. Another alloy B is formed by mixing silver and platinum in the ratio 3 : 4. An alloy C is obtained by mixing alloys A and B in a certain ratio such that the ratio of gold and platinum in alloy C is 5 : 6.
To Find : Which of the following correctly represents the share of silver in alloy C.
Solution:
An alloy A is formed by mixing gold and silver in the ratio 2 : 1
=> Gold = 2X and Silver = X
Another alloy B is formed by mixing silver and platinum in the ratio 3 : 4
=> Silver = 3Y and Platinum = 4Y
alloy C is obtained by mixing alloys A and B in a certain ratio such that
the ratio of gold and platinum in alloy C is 5 : 6
Let say k : 1 ratio in A : B
=> Gold = 2kX , Silver = kX + 3Y , Platinum = 4Y
2kX : 4Y = 5 : 6
=> kX = 5Y/3
Gold = 2kX = 2 (5Y/3) = 10Y/3
, Silver =5Y/3 + 3Y = 14Y/3
Platinum = 4Y
Total = 10Y/3 + 14Y/3 + 4Y = 36Y/3 = 12Y
share of silver in alloy C. = (14Y/3) / 12Y = 7 / 18
share of silver in alloy C. = 7 : 18
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