Question:
A shop, which sold same marked price shirts, announced an offer - if one buys three shirts then the fourth shirt is sold at a discounted price of ₹ 100 only. Patel took the offer. He left the shop with 20 shirts after paying ₹ 20,000. What is the marked price of a shirt?
A shop, which sold same marked price shirts, announced an offer - if one buys three shirts then the fourth shirt is sold at a discounted price of ₹ 100 only. Patel took the offer. He left the shop with 20 shirts after paying ₹ 20,000. What is the marked price of a shirt?
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In offer-based arithmetic problems, always group purchases according to the offer cycle (like here in blocks of 4). This simplifies the problem and avoids mistakes in counting discounts.
Updated On: Aug 23, 2025
- ₹ 1260
- ₹ 1300
- ₹ 1350
- ₹ 1400
- ₹ 1500
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The Correct Option is B
Solution and Explanation
Step 1: Understanding the offer
The shop has an offer: buy 3 shirts at full marked price (M), and get the 4th shirt at a discounted price of only ₹ 100.
Thus, the cost of every block of 4 shirts = \(3M + 100\).
Step 2: Finding how many sets of 4 Patel bought
Patel bought a total of 20 shirts.
Since the offer works in sets of 4 shirts, we divide:
\[ 20 \div 4 = 5 \] So, Patel availed the offer exactly 5 times.
Step 3: Writing total cost equation
Cost of 1 set of 4 shirts = \(3M + 100\).
Cost of 5 sets (20 shirts) = \(5 \times (3M + 100)\).
We are told this equals ₹ 20,000.
So, \[ 5(3M + 100) = 20000 \]
Step 4: Simplifying
Divide both sides by 5:
\[ 3M + 100 = 4000 \] Subtract 100:
\[ 3M = 3900 \] Divide by 3:
\[ M = 1300 \]
Step 5: Final Answer
The marked price of each shirt is ₹ 1300.
\[ \boxed{1300} \]
The shop has an offer: buy 3 shirts at full marked price (M), and get the 4th shirt at a discounted price of only ₹ 100.
Thus, the cost of every block of 4 shirts = \(3M + 100\).
Step 2: Finding how many sets of 4 Patel bought
Patel bought a total of 20 shirts.
Since the offer works in sets of 4 shirts, we divide:
\[ 20 \div 4 = 5 \] So, Patel availed the offer exactly 5 times.
Step 3: Writing total cost equation
Cost of 1 set of 4 shirts = \(3M + 100\).
Cost of 5 sets (20 shirts) = \(5 \times (3M + 100)\).
We are told this equals ₹ 20,000.
So, \[ 5(3M + 100) = 20000 \]
Step 4: Simplifying
Divide both sides by 5:
\[ 3M + 100 = 4000 \] Subtract 100:
\[ 3M = 3900 \] Divide by 3:
\[ M = 1300 \]
Step 5: Final Answer
The marked price of each shirt is ₹ 1300.
\[ \boxed{1300} \]
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