-    Let C.P be Rs.x  then,
  (107.5 % of x) - (97.5 % of x) = 100
  => 10% of x = 100
  => x =1000
  ∴ desired S.P = 112.5 % of Rs. 100
  = Rs.(225/2 x 1/100 x 1000) =Rs. 1125

To gain 12.5%, the dealer needs to sell the article for Rs.1125. To calculate this, we need to use the concepts of profit and loss.

Profit and Loss:
Profit and Loss is a calculation which helps to ascertain the gain or loss made by a person on a particular transaction. Profit is the gain made on the transaction and loss is the amount lost on the transaction.

Formula:
The formula to calculate the profit or loss is given by
Profit/Loss = (SP - CP) / CP * 100
Where SP = Selling Price and CP = Cost Price

Given:
A dealer sold an article at a loss of 2.5%. Had he sold it for Rs. 100 more, he would have gained 7.5%.

Let CP = Cost Price of the article

Loss = 2.5%

Profit = 7.5%

Calculation:
We need to calculate the Selling Price of the article for the dealer to gain 12.5%.

Let SP = Selling Price of the article

For a loss of 2.5%,

Loss = (SP - CP) / CP * 100
2.5 = (SP - CP) / CP * 100
(SP - CP) / CP * 100 = 2.5 / 100
(SP - CP) / CP = 0.025
SP - CP = 0.025 * CP
SP = 0.025 * CP + CP
SP = 1.025 * CP

For a gain of 7.5%,

Profit = (SP - CP) / CP * 100
7.5 = (SP - CP) / CP * 100
(SP - CP) / CP * 100 = 7.5 / 100
(SP - CP) / CP = 0.075
SP - CP = 0.075 * CP
SP = 0.075 * CP + CP
SP = 1.075 * CP

Now,

For a gain of 12.5%,

Profit = (SP - CP) / CP * 100
12.5 = (SP - CP) / CP * 100
(SP - CP) / CP * 100 = 12.5 / 100
(SP - CP) / CP = 0.125
SP - CP = 0.125 * CP
SP = 0.125 * CP + CP
SP = 1.125 * CP

Therefore, the Selling Price of the article for the dealer to gain 12.5% = 1.125 * CP

Since the Cost Price of the article is given to be Rs. 100 more than the Selling Price of the article,

CP = SP + 100
1.125 * CP = SP + 100
1.125 * (SP + 100) = SP + 100
1.125 * SP + 131.25 = SP + 100
0.125 * SP = -31.25
SP = -31.25 / 0.125
SP = Rs.1125

Hence, to gain 12.5%, the dealer needs to sell the article for Rs.1125.

Therefore, the correct answer is Option D. Rs.1125.

If you think the solution is wrong then please provide your own solution below in the comments section .