Question

A dishonest shopkeeper promises to sell his goods at the same price he bought the product but uses a false weight and thus gains 20%. What is the weight he uses for a kg?
1. 850 gm
2. 900 gm
3. 800 gm
4. 833.33 gm

Answer 1

Correct Answer - Option 4 : 833.33 gm

Given:

A dishonest shopkeeper promises to sell his goods at the same price he bought the product but uses a false weight and thus gains 20%.

Formula used:

Percentage profit = \(\frac{error}{true\ weight\ - \ error}\ \times \ 100\)

Calculations:

Let the error be x gm.

so we have, Percentage profit = \(\frac{error}{true\ weight\ - \ error}\ \times \ 100\)

⇒ \(\frac{x}{1000\ -\ x}\ \times \ 100\ =\ 20\)

⇒ \(\frac{x}{1000\ -\ x}\ =\ \frac{1}{5}\)

⇒ 5x = 1000 - x

⇒ 6x = 1000

⇒ x = 166.67 gm

Thus the weight used = 1000 - 166.67 = 833.33 gm

∴ The weight he uses for a kg is 833.33 gm.