The prices of two metals A and B are in a 4:1 ratio. The cost of A increased by 30%, while the combined cost of A and B increased by 25% to Rs 2125. By what amount did increase?

Given:

Initial price ratio of metal A and B = 4 : 1

Combined cost of A and B after a 25% increase = ₹2125

Increase in the cost of A = 30%

Formula Used:

Let the initial prices of A and B be 4x and x respectively.

Initial combined cost = 4x + x = 5x

Increased combined cost = Initial combined cost + 25% of Initial combined cost

Increased cost of A = Initial cost of A + 30% of Initial cost of A

Increase in the cost of B = Increased combined cost - Increased cost of A - Initial cost of B

Calculations:

Initial combined cost = 5x

Increased combined cost = 5x + 0.25 × 5x = 5x + 1.25x = 6.25x

We are given that the increased combined cost is ₹2125.

6.25x = 2125

x = 2125 / 6.25 = 340

Initial price of A = 4x = 4 × 340 = ₹1360

Initial price of B = x = ₹340

Increased cost of A = 1360 + 0.30 × 1360 = 1360 + 408 = ₹1768

Increased combined cost = ₹2125

Increased cost of B = Increased combined cost - Increased cost of A

Increased cost of B = 2125 - 1768 = ₹357

Increase in the cost of B = Increased cost of B - Initial cost of B

Increase in the cost of B = 357 - 340 = ₹17

∴ The cost of B increased by ₹17.