A dealer purchased an oven for ₹605. After allowing a discount of 45% on its marked price, he still gains 37%. Find the marked price of the oven.​

Correct option is D

Given:

Cost price (C.P) of the oven = ₹605

Discount allowed = 45%

Gain = 37%

Formula Used:

S.P = $$\text{M.P} \times \left(1 - \frac{\text{Discount\%}}{100}\right)$$​​

Gain% = $$\frac{\text{S.P} - \text{C.P}}{\text{C.P}} \times 100$$​​

Solution:

Selling Price (S.P) using the gain formula:

​$$37 = \frac{\text{S.P} - 605}{605} \times 100$$​​

​$$37 = \frac{\text{S.P} - 605}{6.05}$$​​

​$$S.P - 605 = 37 \times 6.05 = 223.85$$​​

S.P = 605 + 223.85 = ₹828.85

Marked Price (M.P) using the discount formula:

​$$828.85 = \text{M.P} \times \left(1 - \frac{45}{100}\right)$$​​

​$$828.85 = \text{M.P} \times 0.55$$​​

M.P = $$\frac{828.85}{0.55}$$​ = ₹1507

The marked price of the oven is ₹1507 

Alternate Solution: ​

As dealer purchase oven at ₹605 

CP = 605 

Now, Using formula

​$$\frac{MP}{CP} =\frac{100 + profit}{100-discount} \\ \ \\ \frac{MP}{605} =\frac{137}{55} \\ \ \\ MP = \frac{605 \times 137}{55} = ₹1507$$​​