Explanation:

Let's break down the information:

- Total coins: 1510

- Bag A: 580 coins

- Bag B: 510 coins

- Bag C: 1510 - 580 - 510 = 420 coins

- Copper coins in A : Copper in B : Gold in C = 3 : 2 : 4

- Let them be 3x, 2x, 4x

- Silver in B = Copper in B + 60 = 2x + 60

- Gold in B is 25% less than silver in A. If silver in A = y, then Gold in B = y - y/4 = 0.75y

- Total gold coins = 570

- Ratio total copper : total silver = 20 : 27

Let’s solve step-by-step:

Step 1: Find x (using copper ratio and gold in C)

- 3x (A copper), 2x (B copper), 4x (C gold)

Step 2: Express everything in terms of x and y

- A: Gold (A), Silver (A=y), Copper (A=3x), Total = 580

So Gold (A) = 580 - y - 3x

- B: Gold (B=0.75y), Silver (B=2x+60), Copper (B=2x), Total = 510

So: 0.75y + (2x+60) + 2x = 510

=> 0.75y + 4x + 60 = 510

=> 0.75y + 4x = 450 ........(1)

- C: Gold (C=4x), Silver (C=z), Copper (C), Total = 420

So: 4x + z + (copper C) = 420

Step 3: Total gold coins = 570

- Gold A + Gold B + Gold C = 570

- Gold A = 580 - y - 3x

So: (580 - y - 3x) + 0.75y + 4x = 570

=> 580 - y - 3x + 0.75y + 4x = 570

=> 580 - y + 0.75y - 3x + 4x = 570

=> 580 - 0.25y + x = 570

=> x - 0.25y = 570 - 580 = -10

=> x = 0.25y - 10.............(2)

Step 4: Solve for x and y using equations (1) and (2)

Substitute x = 0.25y - 10 into equation (1):

0.75y + 4x = 450

0.75y + 4*(0.25y - 10) = 450

0.75y + y - 40 = 450

1.75y = 450 + 40 = 490

y = 490/1.75 = 280

So y = 280

Now x = 0.25*280 - 10 = 70 - 10 = 60

So,

A copper = 3x = 180

B copper = 2x = 120

C gold = 4x = 240

Silver in B = 2x + 60 = 120 + 60 = 180

B gold = 0.75y = 0.75*280 = 210

Step 5: Find silver in C (z)

Total coins in C = 420

C gold = 240

Let C silver = z

C copper = 420 - 240 - z = 180 - z

Step 6: Total silvers calculation

A silver = y = 280

B silver = 180

C silver = z

Total silver = 280 + 180 + z = 460 + z

Step 7: Total copper calculation

A copper = 180

B copper = 120

C copper = 180 - z

Total copper = 180 + 120 + (180 - z) = 480 - z

Step 8: Ratio total copper: silver = 20:27

(480 - z)/(460 + z) = 20/27

Cross-multiplied:

27(480 - z) = 20(460 + z)

12960 - 27z = 9200 + 20z

12960 - 9200 = 27z + 20z

3760 = 47z

z = 3760/47 = 80

Step 9: Silver in B + C = 180 (B) + 80 (C) = 260

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## Summary of key points:

- The number of coins in each bag, as well as copper, silver, and gold coins, were deduced step by step.

- Using the ratios and constraints, each bag’s coin types were expressed algebraically and solved.

- The sum of silver coins in B and C = 180 + 80 = 260.

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Correct Option: 2 (260)