Question:easy

A dealer buys an article for Rs. 380.00. What price should he mark so that after allowing a discount of 5% he still makes a profit of 25% on the article?

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Discount is on the marked price, profit is on the cost price. Set 380 times 1.25 equal to MP times 0.95 and solve for MP.
Updated On: Jul 17, 2026
  • Rs. 500
  • Rs. 475
  • Rs. 95
  • Rs. 465
Show Solution

The Correct Option is A

Solution and Explanation

Step 1: Build one chain formula.
Going from cost price to marked price and back down to selling price is a chain of two multipliers.
\[ CP \times (1 + \text{profit}) = MP \times (1 - \text{discount}) \]
This single line captures both conditions at once, so no intermediate value gets forgotten.

Step 2: Put in the numbers.
Profit is 0.25 and discount is 0.05, cost price is 380.
\[ 380 \times 1.25 = MP \times 0.95 \]
\[ 475 = 0.95 \, MP \]

Step 3: Isolate MP.
\[ MP = \frac{475}{0.95} = \frac{47500}{95} = 500 \]

Step 4: Sanity check with ratios.
Another way to see it: $\dfrac{MP}{CP} = \dfrac{1.25}{0.95} = \dfrac{125}{95} = \dfrac{25}{19}$.
So $MP = 380 \times \dfrac{25}{19}$. Since $380 = 19 \times 20$, this is $20 \times 25 = 500$. The 19 cancels cleanly, which is the sign that 380 was chosen deliberately.

Step 5: Eliminate the wrong choices.
If the mark were Rs. 475, the customer would pay $475 \times 0.95 = 451.25$, giving a profit of only about 18.75%. Too low.
Rs. 95 is smaller than the cost price of Rs. 380, so it would be a loss, not a profit.
Rs. 465 gives $465 \times 0.95 = 441.75$, well short of the Rs. 475 the dealer needs.

Final Answer:
The marked price must be Rs. 500. \[ \boxed{\text{Rs. } 500} \]
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