Question

Let Cost Price = C.P. and Selling Price = S.P. Then Match List - I with List - II.

Choose the correct answer from the options given below:

• A. A-II, B-I, C-III, D-IV
• B. A-III, B-IV, C-II, D-I
• C. A-III, B-IV, C-I, D-II
• D. A-I, B-II, C-IV, D-III

Hint:

Always remember that profit or loss percentages are calculated with the Cost Price (C.P.) as the base, unless stated otherwise.
Therefore, the formulas for both Gain% and Loss% must have C.P. in the denominator, which immediately links A to III and B to IV.

Answer 1

The Correct Option is C

Step 1: Understanding the Question:
This question tests basic, fundamental mathematical formulas of Profit and Loss.
We need to match the standard expressions for Gain percentage, Loss percentage, Selling Price, and Cost Price with their mathematical formulations.

Step 2: Detailed Explanation:

• Gain% (A): Gain percent is defined as the profit made divided by the Cost Price, multiplied by 100. \[ \text{Gain}\% = \frac{\text{Gain} \times 100}{\text{C.P.}} \] This matches with formula III.

• Loss% (B): Loss percent is defined as the loss incurred divided by the Cost Price, multiplied by 100. \[ \text{Loss}\% = \frac{\text{Loss} \times 100}{\text{C.P.}} \] This matches with formula IV.

• S.P. (C): When an item is sold at a loss, the Selling Price is calculated by reducing the Cost Price by the loss percentage. \[ \text{S.P.} = \frac{(100 - \text{Loss}\%)}{100} \times \text{C.P.} \] This matches with formula I.

• C.P. (D): When an item is sold at a gain, the Cost Price can be calculated using the Selling Price and the Gain percentage. \[ \text{C.P.} = \frac{100}{(100 + \text{Gain}\%)} \times \text{S.P.} \] This matches with formula II.

Step 3: Final Answer:
The matching combination is:
A $\rightarrow$ III
B $\rightarrow$ IV
C $\rightarrow$ I
D $\rightarrow$ II
This sequence corresponds to option (C).