A dishonest dealer professes to sell his goods at cost price but uses a false weight and thus gains 15%. For a kilogram, he uses a weight of _________ (rounded off to one digit after decimal).

Question

Question

This question was previously asked in

SSC CGL 2022 Tier-I Official Paper (Held On : 12 Dec 2022 Shift 2)

Answer 1

Given:

A dishonest dealer professes to sell his goods at cost price but uses a false weight and thus gains 15%.

Concept used:

Profit% = \({(Selling\ Price\ -\ Cost\ Price) \over Cost\ Price} \times 100\%\)

Calculation:

Let the price of 1 gm of the article be Rs. 1.

Let's suppose, he uses the weight of Q gm for 1 kilogram.

Cost price of Q gm = Q × 1 = Rs. Q

Selling price of Q gm = 1000 × 1 = Rs. 1000

According to the concept,

\(\frac {1000 - Q}{Q} \times 100\) = 15

⇒ 15Q = 100000 - 100Q

⇒ 115Q = 100000

⇒ Q = 100000/115

⇒ Q = 869.56

⇒ Q ≈ 869.6

∴ For a kilogram, he uses a weight of 869.6 gm.

Shortcut Trick

In terms of price the dealer sells at CP, then CP : SP = 1 : 1, at the end gain 15% through faulty weight,

So, x : y = (23 × 1)/(20 × 1) = 23 : 20

Now, 23 unit → 1000 g then, 20 unit → 1000/23 × 20 = 869.6 g