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The monthly sales of a product from January to April were 120, 135, 150 and 165 units, respectively. The cost price of the product was Rs. 240 per unit, and a fixed marked price was used for the product in all the four months. Discounts of 20%, 10% and 5% were given on the marked price per unit in January, February and March, respectively, while no discounts were given in April. If the total profit from January to April was Rs. 138825, then the marked price per unit, in rupees, was

Solution

✅ Correct Option: 4

We're told:
Monthly sales (in units): Jan =120= 120, Feb =135= 135, Mar =150= 150, Apr =165= 165
Cost price =Rs. 240= Rs.\ 240 per unit
Discounts on marked price: Jan =20%= 20\%, Feb =10%= 10\%, Mar =5%= 5\%, Apr =0%= 0\%
Total profit from Jan to Apr =Rs. 138825= Rs.\ 138825

We need to find the fixed Marked Price (MP) per unit.


Total units sold =120+135+150+165=570= 120 + 135 + 150 + 165 = 570

Total Cost =570×240=Rs. 136800= 570 \times 240 = Rs.\ 136800


When a discount is given on the marked price, the selling price per unit becomes MP×(1−Discount%/100)MP \times (1 - \text{Discount\%}/100). So the revenue from each month is:

Jan: 120×0.80×MP=96 MP120 \times 0.80 \times MP = 96\,MP

Feb: 135×0.90×MP=121.5 MP135 \times 0.90 \times MP = 121.5\,MP

Mar: 150×0.95×MP=142.5 MP150 \times 0.95 \times MP = 142.5\,MP

Apr: 165×1.00×MP=165 MP165 \times 1.00 \times MP = 165\,MP

Total Revenue =(96+121.5+142.5+165)×MP=525 MP= (96 + 121.5 + 142.5 + 165) \times MP = 525\,MP


Using Profit == Total Revenue −- Total Cost:

138825=525×MP−136800138825 = 525 \times MP - 136800

525×MP=138825+136800=275625525 \times MP = 138825 + 136800 = 275625

MP=275625525MP = \dfrac{275625}{525}

MP=525MP = 525


The marked price per unit is Rs. 525Rs.\ 525.

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