Ankita sold her watch at 5% loss. If she had sold it for Rs. 300 more, she would have gained 5%. Find the selling price of the watch.

Question

Question

This question was previously asked in

SSC CGL 2023 Tier-I Official Paper (Held On: 24 Jul 2023 Shift 1)

Answer 1

Given:

Firstly sold at a loss of 5%

Secondly sold at a profit of 5%

Formula used:

S.P = (100 + P%)/100 * CP

S.P = (100 - L%)/100 * CP

Where, S.P = Selling Price, C.P = Cost Price, P = Profit, L = Loss

Calculation:

Firstly sold at a loss of 5%

Then, S.P₁ = (100 - 5%)/100 * CP

⇒ S.P₁ = 95/100 × C.P

Secondly sold at a profit of 5%

Then, S.P₂ = (100 + P%)/100 * CP

⇒ S.P2 = 105/100 × C.P

According to the question:

S.P₂- S.P₁ = (105/100 × C.P) - (95/100 × C.P)

⇒ S.P1 - S.P2 = 105% C.P - 95% C.P

⇒ 300 = 10% × C.P

⇒ C.P = [(300/10) × 100] = Rs. 3000

S.P = 95/100 × 3000

⇒ S.P = 2850

∴ The selling price is Rs. 2850.

Shortcut Trick

105% - 95% = 300

⇒ 10% = 300

⇒ 1% = 30

⇒ 100% = 3000

⇒ 95% = 2850