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A discount of 30% on the marked price of...

A discount of 30% on the marked price of a shirt enables a man to purchasea tie also, which costs him ₹ 210. How much did the man pay for the shirt

A

₹540

B

₹490

C

₹630

D

₹700

Text Solution

AI Generated Solution

The correct Answer is:
To solve the problem step by step, let's break it down: ### Step 1: Understand the Problem The problem states that a man receives a 30% discount on the marked price of a shirt, allowing him to buy a tie that costs ₹210. We need to find out how much he paid for the shirt after the discount. **Hint:** Identify the key components: the discount percentage, the cost of the tie, and the relationship between the shirt and tie costs. ### Step 2: Assume the Marked Price Let's assume the marked price (MP) of the shirt is ₹100. This makes calculations easier since we can easily calculate the discount. **Hint:** Starting with a simple assumption (like MP = ₹100) can simplify the calculations. ### Step 3: Calculate the Discount The discount on the shirt is 30% of the marked price: \[ \text{Discount} = 30\% \text{ of } 100 = \frac{30}{100} \times 100 = ₹30 \] **Hint:** Remember that the discount is a percentage of the marked price. ### Step 4: Determine the Selling Price of the Shirt The selling price (SP) of the shirt after applying the discount is: \[ \text{SP} = \text{MP} - \text{Discount} = 100 - 30 = ₹70 \] **Hint:** The selling price is what you pay after the discount is applied. ### Step 5: Relate the Discount to the Cost of the Tie The discount of ₹30 allowed the man to buy a tie costing ₹210. This means that the ₹30 discount is equivalent to the cost of the tie. **Hint:** Understand the relationship between the discount and the tie's cost. ### Step 6: Set Up a Proportion We can set up a proportion to find out how much the shirt costs in relation to the tie: \[ \text{If } 30 \text{ (discount)} \text{ corresponds to } 210 \text{ (cost of tie)}, \] we can find out how much ₹70 (the selling price of the shirt) corresponds to: \[ \frac{30}{210} = \frac{70}{x} \] **Hint:** Setting up a proportion helps to relate different quantities. ### Step 7: Solve for x Cross-multiplying gives: \[ 30x = 70 \times 210 \] \[ 30x = 14700 \] \[ x = \frac{14700}{30} = 490 \] **Hint:** Cross-multiplication is a powerful tool for solving proportions. ### Step 8: Conclusion Thus, the man paid ₹490 for the shirt. **Final Answer:** The man paid ₹490 for the shirt.
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