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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. Find the initial price of x.


1. 1790
2. 1760
3. 1810
4. 1880

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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

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