Problem Solving

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

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

Solution:

Let the amount of tin in the alloy be x. Then, the amount of silver in the alloy is 20 - x.

Since 10 kg of tin loses 1.375 kg in the water, x kg of tin loses x * (1.375/10) = 0.1375x kg in the water. Since 5 kg of silver loses 0.375 kg in the water, (20 - x) kg of silver loses (20 - x)*(0.375/5) = (20 - x) * 0.075 = 1.5 - 0.075x kg in the water.

Since the total weight lost in the water is 2, we have:

0.1375x + 1.5 - 0.075x = 2

0.0625x = 0.5

x = 0.5/0.0625 = 8

We see that the alloy contains x = 8 kg of tin and (20 - x) = 12 kg of silver. Thus, the ratio of tin to silver in the alloy is 8/12 = 2/3.

Answer: E