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Mathematics

Assertion (A) : If selling price of an article is ₹ 400 gaining 14\dfrac{1}{4} of its C.P., then gain% = 25%.

Reason (R) : Loss = C.P.×Loss%100\dfrac{\text{C.P.} \times \text{Loss}\%}{100}.

  1. Both A and R are correct, and R is the correct explanation for A.

  2. Both A and R are correct, and R is not the correct explanation for A.

  3. A is true, but R is false.

  4. A is false, but R is true.

Profit, Loss & Discount

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Answer

Let the C.P. be ₹ a.

Gain = 14\dfrac{1}{4} of its C.P = 14\dfrac{1}{4} x a

Using the formula,

S.P. = Gain + C.P.

⇒400=14×a+a⇒400=a+4a4⇒400=5a4⇒a=4×4005⇒a=16005⇒a=₹320\Rightarrow 400 = \dfrac{1}{4} \times a + a \\[1em] \Rightarrow 400 = \dfrac{a + 4a}{4} \\[1em] \Rightarrow 400 = \dfrac{5a}{4} \\[1em] \Rightarrow a = \dfrac{4 \times 400}{5} \\[1em] \Rightarrow a = \dfrac{1600}{5} \\[1em] \Rightarrow a = ₹320

Gain = S.P. - C.P. = ₹ 400 - ₹ 320 = ₹ 80.

Gain %=GainC.P.×100%=80320×100%=8000320%=25%\text{Gain \%}= \dfrac{\text{Gain}}{\text{C.P.}} \times 100\%\\[1em] = \dfrac{80}{320} \times 100\%\\[1em] = \dfrac{8000}{320}\%\\[1em] = 25 \%

So, assertion (A) is true.

By formula,

Loss% = C.P.×Loss%100\dfrac{\text{C.P.} \times \text{Loss}\%}{100}

So, reason (R) is true but reason (R) does not explains assertion (A).

Hence, option 2 is the correct option.

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