A trader marked his goods at 25% above the cost price. He sold one thi

1.	A trader marked his goods at 25% above the cost price. He sold one third of the goods at the marked price, one quarter at a discount of 10% on the marked price and the rest at a discount of 30% on the marked price. His total gain is1). 6.25%2). 4.75%3). 12.5%4). 13%
Answer» LET the total number of ITEMS = 12 (L.C.M of 4 and 3 is 12) Let COST Price of each item = Rs.x ⇒ Total Cost Price = 12x Marked Price of each item = 1.25x As, one third of the stock is sold at the marked price, S.P₁ = (1/3) × 12 × 1.25x = 5x As, one quarter of the stock is sold at a discount of 10% on the marked price, S.P₂ = (1/4) × 12 × 0.9 × 1.25x = 3.375x As, the rest of the stock is sold at a discount of 30% on the marked price, S.P₃ = 5 × 0.7 × 1.25x = 4.375x Total S.P = S.P₁ + S.P₂ + S.P₃ ⇒ S.P = 5x + 3.375x + 4.375x = 12.75x Total C.P = 12x Total S.P = 12.75x Profit = 0.75x Profit Percentage = (0.75/12) × 100 = 6.25%

A trader marked his goods at 25% above the cost price. He sold one third of the goods at the marked price, one quarter at a discount of 10% on the marked price and the rest at a discount of 30% on the marked price. His total gain is1). 6.25%2). 4.75%3). 12.5%4). 13%

Answer»

LET the total number of ITEMS = 12 (L.C.M of 4 and 3 is 12)

Let COST Price of each item = Rs.x

⇒ Total Cost Price = 12x

Marked Price of each item = 1.25x

As, one third of the stock is sold at the marked price,

S.P₁ = (1/3) × 12 × 1.25x = 5x

As, one quarter of the stock is sold at a discount of 10% on the marked price,

S.P₂ = (1/4) × 12 × 0.9 × 1.25x = 3.375x

As, the rest of the stock is sold at a discount of 30% on the marked price,

S.P₃ = 5 × 0.7 × 1.25x = 4.375x

Total S.P = S.P₁ + S.P₂ + S.P₃

⇒ S.P = 5x + 3.375x + 4.375x = 12.75x

Total C.P = 12x

Total S.P = 12.75x

Profit = 0.75x

Profit Percentage = (0.75/12) × 100 = 6.25%

Discussion

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