In a compound weighing 1200 gm, metals A and B are in the ratio 5 : 7 and in another compound weighing 800 gm, metals A and B are in the ratio 3 : 1. Find the difference between weight of metal A and metal B in the third compound which is the mixture of compound 1 and compound 2.

In a compound weighing 1200 gm, metals A and B are in the ratio 5 : 7 and in another compound weighing 800 gm, metals A and B are in the ratio 3 : 1. Find the difference between weight of metal A and metal B in the third compound which is the mixture of compound 1 and compound 2. Correct Answer 200 gm

Given:

In a compound weighing 1200 gm, metals A and B are in the ratio 5 : 7 and in another compound weighing 800 gm, metals A and B are in the ratio 3 : 1

Calculation:

Let the weight of metals A and B in compound 1 be 5x and 7x

Then 5x + 7x = 1200 gm

⇒ 12x = 1200 gm

⇒ x = 100 gm

∴ Weight of A and B in compound 1 is 500 gm and 700 gm respectively.

Let the weight of metals A and B in compound 2 be 3y and 1y

Then 3y + y = 800 gm

⇒ 4y = 800 gm

⇒ y = 200 gm

∴ Weight of A and B in compound 2 is 600 gm and 200 gm respectively.

Thus, Total weight of A = 500 gm + 600 gm = 1100 gm

And, Total weight of B = 700 gm + 200 gm = 900 gm

∴ Difference between weight of these two metals is 1100 gm - 900 gm = 200 gm