The reduction of 20% in the price of rice enables a person to obtain 50 kg more for Rs. 450. Find the original price of rice per kg.

Question

Question

This question was previously asked in

SSC CGL 2022 Tier-I Official Paper (Held On : 02 Dec 2022 Shift 2)

Answer 1

Given:

The reduction of 20% in the price of rice enables a person to obtain 50 kg more for Rs. 450.

Concept used:

Incremented/Reduced value = Initial value (1 ± change%)

Calculation:

Let's suppose, originally for Rs. 450, one could get Q kg rice.

Now, for Rs. 450, one can get (Q + 50) kg rice.

According to the question,

\(\frac {450}{Q} × (1 - 20\%) = \frac {450}{Q + 50}\)

⇒ \(\frac {1}{Q} × 0.8 = \frac {1}{Q + 50}\)

⇒ \(\frac {1}{Q} × \frac {4}{5} = \frac {1}{Q + 50}\)

⇒ 4Q + 200 = 5Q

⇒ Q = 200

Now, the original price of rice (per kg) = 450/200 = Rs. 2.25

∴ The original price of rice per kg is Rs. 2.25.

Shortcut Trick

We know, 20% = 1/5,

Consumption difference (5 - 4) = 1 unit → 50 kg

Then, 4 unit → 50 × 4 = 200 kg

Now, price of 200 kg is 450

Then price of 1 kg is 450/200 = Rs.2.25