The following question has two statements. Study the question and the statements and decide which of the statement(s) is necessary to answer the question. While purchasing a mat, if salesman gives a discount of x% on the marked price, he will get profit of 2x% on CP. Determine whether his profit is more than 40% I) The marked price of mat is more than 1.8 times its CP. II) MP of mat is more than 1.7 times its CP.?

Question

The following question has two statements. Study the question and the statements and decide which of the statement(s) is necessary to answer the question. While purchasing a mat, if salesman gives a discount of x% on the marked price, he will get profit of 2x% on CP. Determine whether his profit is more than 40% I) The marked price of mat is more than 1.8 times its CP. II) MP of mat is more than 1.7 times its CP.?

Only I
Only II
Both I and II
Either I or II
None of the above

LohaHridoy

4 views

2025-01-04 04:42

1 Answers

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AhmedNazir · Accepted Answer · 2022-09-04T04:29:57+06:00

Option 4 : Either I or II

Given, Discount = x% of MP

Profit = 2x% of CP

Considering statement I,

MP = CP + 1.8CP = 2.8CP

⇒ MP/CP = 2.8

SP = MP - discount = CP + Profit

⇒ MP - x% of MP = CP + 2x% of CP

⇒ (100 - x)/100 × MP = (100 + 2x)/100 × CP

⇒ (100 - x) × 2.8 = (100 + 2x)

⇒ 280 - 2.8x = 100 + 2x

⇒ 180 = 4.8x

⇒ x = 180/4.8 = 37.5%

⇒ Profit = 2x = 75% > 40%

Considering statement II,

MP = CP + 1.7CP = 2.7CP

⇒ MP/CP = 2.7

SP = MP - discount = CP + Profit

⇒ MP - x% of MP = CP + 2x% of CP

⇒ (100 - x)/100 × MP = (100 + 2x)/100 × CP

⇒ (100 - x) × 2.7 = (100 + 2x)

⇒ 270 - 2.7x = 100 + 2x

⇒ 170 = 4.7x

⇒ x = 170/4.7 ≅ 36.2%

⇒ Profit = 2x = 72.4% > 40%

∴ The question can be answered using either of the statements