A man sells an article at a proﬁt of 35%. If he had bought it for 15

1.	A man sells an article at a proﬁt of 35%. If he had bought it for 15% less price and sold it for Rs. 32 less, then he would have gained 40%. What is the initial cost price (in Rs) of the article?1). 2502). 2003). 3004). 400
Answer» Case 1: Let the cost price be ‘C’ Since the man sold the article at a profit of 35% ⇒ Selling Price (S) = Cost Price × (1 + Profit%) = C × (1 + 35%) = 1.35C ⇒ S = 1.35C---- (Equation 1) Case 2: In case the cost price is 15% less = C - (15%C) = C - 0.15C = 0.85C ⇒ Selling Price = S - 32 ⇒ Selling Price = Cost Price × (1 + Profit%) ⇒ S - 32 = 0.85C × (1 + 40%)---- (Equation 2) Substituting the VALUE of ‘S’ from Equation 1 in Equation 2, we get ⇒ 1.35C - 32 = 0.85C (1.4) ⇒ 1.35C - 32 = 1.19C ⇒ 1.35C - 1.19C = 32 ⇒ 0.16C = 32 ⇒ C = 32/0.16 = 200 ∴ Initial Cost price = 200

A man sells an article at a proﬁt of 35%. If he had bought it for 15% less price and sold it for Rs. 32 less, then he would have gained 40%. What is the initial cost price (in Rs) of the article?1). 2502). 2003). 3004). 400

Answer»

Case 1:

Let the cost price be ‘C’

Since the man sold the article at a profit of 35%

⇒ Selling Price (S) = Cost Price × (1 + Profit%) = C × (1 + 35%) = 1.35C

⇒ S = 1.35C---- (Equation 1)

Case 2:

In case the cost price is 15% less = C - (15%C) = C - 0.15C = 0.85C

⇒ Selling Price = S - 32

⇒ Selling Price = Cost Price × (1 + Profit%)

⇒ S - 32 = 0.85C × (1 + 40%)---- (Equation 2)

Substituting the VALUE of ‘S’ from Equation 1 in Equation 2, we get

⇒ 1.35C - 32 = 0.85C (1.4)

⇒ 1.35C - 32 = 1.19C

⇒ 1.35C - 1.19C = 32

⇒ 0.16C = 32

⇒ C = 32/0.16 = 200

∴ Initial Cost price = 200

Discussion

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