Correct Answer - Option 4 : 1880
Given:
The difference between the price of two goods x and y is 310.
The price of x is increases by 40% and the price of y increases by 30%.
The difference in the increased price of x and y is 591, where the price of x is more than y in both the cases.
Formula:
Profit or Gain = Selling price – Cost Price
Loss = Cost Price – Selling Price
Profit percentage = (Profit/Cost Price) x 100
Loss percentage = (Loss/Cost price) x 100
Calculation:
Let price of x be a and y be b
a – b = 310
⇒ a = 310 + b ----(i)
now,
a × 140% - b × 130% = 591
⇒ 7a/5 – 13b/10 = 591
⇒ 14a – 13b = 5910
⇒ 14(310 + b) - 13b = 5910 [From (i)]
⇒ 4340 + 14b - 13b = 5910
⇒ b = 1570
From (i),
a = 1570 + 310 = 1880
∴ initial price of x is Rs. 1880