A dealer marked the price of an item at 50% above the cost price. He allowed two successive discounts of 30% and 25% to a
particular customer. As a result, he incurred a loss of Rs 850. At what price did he sell the item to the said customer?
This questions was previously asked in
SSC MTS 27th October 2021 Shift-3
Explanation:
Let's break down the problem:
- The cost price (CP) is the initial price at which the dealer bought the item.
- The marked price (MP) is 50% above the CP.
- So, MP = 1.5 × CP.
- The dealer gives two successive discounts of 30% and 25%.
- Effective discount = 1 - (0.7 × 0.75) = 0.475 or 47.5%.
- Therefore, the selling price (SP) = MP × (1 - 0.475).
- As a result of these discounts, the dealer incurs a loss of Rs 850.
- Loss = CP - SP = Rs 850.
We need to find the SP.
- SP = MP × 0.525 = 1.5 × CP × 0.525 = 0.7875 × CP.
- CP - 0.7875 × CP = 850.
- 0.2125 × CP = 850.
- CP = 850 / 0.2125 = Rs 4,000.
- SP = 0.7875 × 4,000 = Rs 3,150.
So, the selling price of the item is Rs 3,150.
- Option 1: Rs 3,150
- Option 2: Rs 3,250
- Option 3: Rs 3,050
- Option 4: Rs 3,200
. The correct selling price is Rs 3,150. ??
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By: santosh