Question

A man bought an article and sold it at a gain of 10%. If he had bought the article at 20% less and sold it for Rs. 1,000 more, he would have made a profit of 40%. The cost price of the article (in Rs.) is:
1. 60,000
2. 50,000
3. 40,000
4. 25,000

Answer 1

Correct Answer - Option 2 : 50,000

Given:

Profit = 10%

New profit% = 40%

Concept used:

SP = (100 + Profit%)/100 × CP

Calculation:

Let original CP of the article was x.

Case 1:

SP = (100 + Profit%)/100 × CP

⇒ SP = (100 + 10%)/100 × x

⇒ SP = 11x/10

Case2:

New CP is 20% less than original CP and sold it for Rs. 1000 more

New CP = x – 20% of x

⇒ New CP = x – 20/100 × x

⇒ New CP = 80/100 × x

⇒ New CP = 4/5 × x

According to the question,

(SP + 1000) – New CP = 40% of New CP

⇒ (11x/10 + 1000) – 4x/5 = 40% of 4x/5

⇒ 11x/10  – 4x/5 + 1000 = 40/100 × 4x/5

⇒ (11x – 8x)/10 – 8x/25 = -1000

⇒ 3x/10 – 8x/25 = -1000

⇒ (15x – 16x)/50 = -1000

⇒ -x/50 = -1000

⇒ x = Rs. 50000

∴ The Cost Price of article is Rs. 50000.