M7MBA wrote: ↑Sun Mar 14, 2021 5:30 am
A 20 kg metal bar made of alloy of tin and silver lost 2 kg of its weight in the water. 10 kg of tin loses 1.375 kg in the water; 5 kg of silver loses 0.375 kg. What is the ratio of tin to silver in the bar?
A. 1/4
B. 2/5
C. 1/2
D. 3/5
E. 2/3
Answer:
E
Source: GMAT Club Tests
Given: 10 kg of tin loses 1.375 kg in the water
This means ONE kg of tin loses 0.1375 kg in the water
Given: 5 kg of silver loses 0.375 kg in the water
This means ONE kg of silver loses 0.075 kg in the water
Let T = the number of kilograms of TIN in the metal bar
Let V = the number of kilograms of SILVER in the metal bar
Since the metal bar weighs 20 kg, we can write:
T + V = 20
Since the metal bar lost 2 kg of its weight in the water, we can write: (water lost from the TIN) + (water lost from the SILVER) = 2 kg
In other words:
0.1375T + 0.075V = 2
We now have the following system of equations:
T + V = 20
0.1375T + 0.075V = 2
Take the top equation and multiply both sides by 0.1375 to get:
0.1375T + 0.1375V = 2.75
0.1375T + 0.075V = 2
Subtract the bottom equation from the top equation to get: 0.0625V = 0.75
Solve: V = 0.75/0.0625 = 12
So, there are
12 kg of silver in the 20 kg metal bar
This means there are
8 kg of tin in the 20 kg metal bar
What is the ratio of tin to silver in the bar?
Tin/Silver =
8/
12 = 2/3
Answer: E
