On selling a wardrobe at ₹3,437, the value of gain is 75% more than the value of loss incurred on selling it at ₹3,338. In order to gain 50%, find the selling price (in ₹).

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This question was previously asked in

RRB NTPC Graduate Level CBT-I Official Paper (Held On: 06 Jun, 2025 Shift 2)

Answer 1

Given:

Selling Price 1 (SP1) = ₹3,437 (results in gain)

Selling Price 2 (SP2) = ₹3,338 (results in loss)

Gain (G) = 75% more than Loss (L)

Required Gain = 50%

Formula used:

Gain = Selling Price - Cost Price (SP - CP)

Loss = Cost Price - Selling Price (CP - SP)

Required SP = CP × \((1 + \frac{Gain\%}{100})\)

Calculations:

Let CP be the Cost Price.

Gain (G) = SP1 - CP = 3437 - CP

Loss (L) = CP - SP2 = CP - 3338

Given, Gain is 75% more than Loss:

G = L + 0.75L

⇒ G = 1.75L

Substitute the expressions for G and L:

3437 - CP = 1.75 × (CP - 3338)

⇒ 3437 - CP = 1.75CP - 1.75 × 3338

⇒ 3437 - CP = 1.75CP - 5841.5

⇒ 3437 + 5841.5 = 1.75CP + CP

⇒ 9278.5 = 2.75CP

⇒ CP = \(\frac{9278.5}{2.75}\)

⇒ CP = ₹3374

Now, to gain 50%, the new Selling Price (SP_new) will be:

SP_new = CP × \((1 + \frac{50}{100})\)

⇒ SP_new = 3374 × (1 + 0.5)

⇒ SP_new = 3374 × 1.5

⇒ SP_new = ₹5061

∴ The selling price to gain 50% is ₹5,061.

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