Find the difference between selling price of article Y and marked price of article X. To find the difference which statement/s is/are required?

(A) Selling price of article X is Rs.140 more than that of article Y and article X is marked up by Rs.264.

(B) Discount given on article Y is Rs.56 more than the profit earned on article X.

(C) Selling price of article Y is Rs.224 more than the cost price of article Y. Discount given on article X is 30% and profit earned on article Y is 40%.

Question

Find the difference between selling price of article Y and marked price of article X. To find the difference which statement/s is/are required?

(A) Selling price of article X is Rs.140 more than that of article Y and article X is marked up by Rs.264.

(B) Discount given on article Y is Rs.56 more than the profit earned on article X.

(C) Selling price of article Y is Rs.224 more than the cost price of article Y. Discount given on article X is 30% and profit earned on article Y is 40%.

Accepted Answer

**Solution:**

1. Let the articles be X and Y corresponding to A and B respectively.

2. From statement (A):
   - Selling price of X ($SP_X$) is Rs.140 more than selling price of Y ($SP_Y$):
     $$SP_X = SP_Y + 140$$
   - Marked price of X ($MP_X$) is Rs.264 more than cost price of X ($CP_X$):
     $$MP_X - CP_X = 264$$

3. From statement (C):
   - Selling price of Y is Rs.224 more than cost price of Y ($CP_Y$):
     $$SP_Y = CP_Y + 224$$
   - Discount on X is 30%, so:
     $$SP_X = 0.7 	imes MP_X$$
   - Profit on Y is 40%, so:
     $$SP_Y = 1.4 	imes CP_Y$$

4. Using (A) and (C) together:
   - From $SP_X = SP_Y + 140$ and $SP_X = 0.7 MP_X$, we get:
     $$0.7 MP_X = SP_Y + 140$$
   - From $MP_X - CP_X = 264$ and $SP_Y = CP_Y + 224$, and $SP_Y = 1.4 CP_Y$, we can relate variables.

5. These two statements provide enough equations to solve for $SP_Y$ and $MP_X$ and hence find the difference $SP_Y - MP_X$.

6. Statement (B) alone or combined with (C) does not provide sufficient information to find the difference.

**Answer:** (b) Both (A) & (C) together

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