A person having bought goods for Rs. 400 sells half of it at a gain of 5%. At what gain percentage must he sell the remainder, so as to gain 25% on the whole?

Question

Question

This question was previously asked in

SSC CGL 2022 Tier-I Official Paper (Held On : 08 Dec 2022 Shift 2)

Answer 1

Given:

A person having bought goods for Rs. 400 sells half of it at a gain of 5%

He has to gain 25% on the whole

Formula used:

Percentage = \(\frac{Profit}{CP}×100\)

Calculations:

As he sell half of it at a gain of 5%

Rs. 200 at a profit of 5%

⇒ SP = 200 + 5% of 200 = 200 + 10 = Rs. 210

Now he has to gain 25% on the whole

⇒ Gain = 400 + 25% of 400 = 400 + 100 = Rs. 500

⇒ Profit he has to earned more = 500 - 210 = Rs. 290

⇒ Profit = 290 - 200 = 90

According to the formula,

⇒ Percentage = \(\frac{90}{200}×100\)= 45%

⇒ Hence, He has to sell the remaining part at 45%

Shortcut Trick

1^st Half of 400 = 200, sells at 5% profit, CP = 200 SP = 210

Final profit on 400, 25% so CP = 400 and SP = 500

So, the 2^nd half CP = 200 and SP = (500 - 210) = 290

Profit% = 90/200 × 100 = 45%