A trader sells two articles, one at a loss of 10% and another at a profit of 15%

Ques - A trader sells two articles, one at a loss of 10% and another at a profit of 15% but finally there is no loss or gain. If the total sale price of these two articles is Rs. 30,000, find the difference between their cost prices :

(a) Rs. 5000

(b) Rs. 6000

(c) Rs. 7500

(d) None of these

Solution - 

If the total sale price of these two articles is Rs. 30,000.

There is no loss or gain.

So,

Total Cost price = Total sale price = 30,000

Let,

C.P of first article = x

S.P of first article  = 0.9x   ___________ (1)

C.P of second article = 30,000 - x

S.P of second article = (30,000 - x)1.15

= 34,500 - 1.15x   ____________ (2)

The S.P of both articles = Rs. 30,000

So,

0.9x + 34,500 - 1.15x = 30,000

- 0.25x = 30,000 - 34,500

- 0.25x = - 4,500

0.25x = 4,500

x = 4,500 / 0.25

x = 18000

C.P of first article = x

C.P of first article = 18,000

C.P of second article = 30,000 - x

C.P of second article = 30,000 - 18000

C.P of second article = 12,000

Therefore,

The difference between their cost prices = 18,000 - 12,000

= 6,000

Hence,

The correct answer is (b) Rs. 6000.

Thank You