Question

Sumit sells an article at a certain price. Had he sold it at fourth-fifth of that selling price, he would have lost 10%. If he sells it for 95% of the original selling price, then the gain percentage will be∶ 
1. \(6\dfrac{8}{9}\)
2. \(6\dfrac{7}{8}\)
3. \(6\dfrac{1}{9}\)
4. \(6\dfrac{1}{8}\)

Answer 1

Correct Answer - Option 2 : \(6\dfrac{7}{8}\)

Given:

If Sumit sells an article at fourth-fifth of the original selling price, he would have lost 10%.

Formulae Used:

If the Selling Price of the article is SP, and 

The Cost Price is CP, then:

Profit% = [(SP – CP)/CP] × 100

Loss% = [(CP – SP)/CP] × 100

Calculation:

Let the original selling price be Rs.x

Let the Cost Price of the article be CP

If selling at a price which is (4/5)^th of the original selling price, then we get:

New Selling Price (SP) = (4/5)x = 0.8x

At this SP, the loss is 10%. Hence, we get:

10 = [(CP – 0.8x)/CP] × 100

⇒ 10CP = 100CP – 80x

⇒ 9CP = 8x

⇒ CP = (8/9)x      ----(i)

Now, when it is sold at an SP, which is 95% of the original SP, we get:

Final SP = (95/100)x = (19/20)x      ----(ii)

Hence, the finally obtained profit is:

Profit% = {[(19/20)x – (8/9)x]/[(8/9)x]} × 100

⇒ Profit% = (11/180) × (9/8) × 100 = (55/8)%

∴ The required profit will be \(6\frac{7}{8}\)%