Question

By selling a sofa set for Rs. 25,800 and a table for Rs. 5,000, a shopkeeper gains 10% on the whole transaction. However, if he sells the sofa set for Rs. 22,500 and the table for its original cost, he loses 5%. What is the original cost of the table?
1. Rs. 3,500
2. Rs. 3,834
3. Rs. 4,750
4. Rs. 4,100

Answer 1

Correct Answer - Option 4 : Rs. 4,100

Given:

SP of sofa set for 1^st transaction = Rs. 25,800

SP of table for 1^st transaction = Rs. 5,000

Gain in 1^st transaction = 10%

SP of sofa set in 2^nd transaction = Rs. 22,500

SP of table for 2^nd transaction = CP

Loss in 2^nd transaction = 5%

Formula used: 

Profit = SP – CP

Loss = CP – SP

Profit % = (SP – CP)/CP × 100

Loss % = (CP – SP)/CP × 100

Calculation:

Total SP in 1^st transaction = SP of sofa set + SP of table

⇒ Total SP in 1^st transaction = 25800 + 5000

⇒ Total SP in 1^st transaction = 30800

Profit % = (SP – CP)/CP × 100

⇒ 10 = (30800 – CP)/CP × 100

⇒ CP = (30800 – CP)10

⇒ CP = 308000 – 10CP

⇒ 11CP = 308000

⇒ CP = 28000

Total CP = Rs. 28,000

Loss = 5% of 28000

⇒ Loss = 5/100 × 28000 = 1400

As, table is sold at cost price in 2^nd transaction

CP of sofa set = 22500 + 1400 = 23900

CP of table = Total CP – CP of sofa set

⇒ CP of table = 28000 – 23900

⇒ CP of table = 4100

∴ Cost price of table is Rs. 4100