Step 1: Calculate Total Cost Price (CP)
Total units sold $= 120 + 135 + 150 + 165 = 570$.
CP per unit $= 240$.
Total CP $= 570 \times 240 = 1,36,800$.
Step 2: Express Total Selling Price (SP) in terms of Marked Price ($M$)
Jan SP $= 120 \times 0.80M = 96M$
Feb SP $= 135 \times 0.90M = 121.5M$
Mar SP $= 150 \times 0.95M = 142.5M$
Apr SP $= 165 \times 1.00M = 165M$
Total SP $= 96M + 121.5M + 142.5M + 165M = 525M$.
Step 3: Equate Profit
$\text{Profit} = \text{Total SP} - \text{Total CP}$
$1,38,825 = 525M - 1,36,800$
$525M = 1,38,825 + 1,36,800 = 2,75,625$
$M = \frac{2,75,625}{525} = \mathbf{525}$.
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