Verified answer

Given data : A jacket was sold at a gain of 5 %. If it has been sold for Rs 1700 less, he would have suffered loss of 10 %.

Solution : Let, selling price be, x

➜ Profit percentage = 5 %

➜ Selling price = x

When,

➜ Loss percentage = 10 %

➜ Selling price = Rs (x - 1700) [a/c to given data]

Now,

➜ Profit % = [Profit * 100]/CP

➜ Profit % = [(SP - CP) * 100]/CP

➜ 5 = [(x - CP) * 100]/CP

➜ CP = [(x - CP) * 100]/5 ----{1}

Simillarly,

➜ Loss % = [Loss * 100]/CP

➜ Loss % = [(CP - SP) * 100]/CP

➜ 10 = [(CP - (x - 1700)) * 100]/CP

➜ CP = [(CP - (x - 1700)) * 100]/10 ----{2}

From eq. {1} and eq. {2}

➜ [(x - CP) * 100]/5 = [(CP - (x - 1700)) * 100]/10

➜ 2 [(x - CP) * 100] = [(CP - (x - 1700)) * 100]

Now, let cost price be y

➜ 2 [(x - y) * 100] = [(y - (x - 1700)) * 100]

➜ (2x - 2y) * 100 = (y - x + 1700) * 100

➜ 200x - 200y = 100y - 100x + 170000

➜ 200x + 100x - 200y - 100y = 170000

➜ 300x - 300y = 170000

➜ 300 * (x - y) = 170000

➜ x - y = 170000/300

➜ x - y = 1700/3

➜ x - y = 566.67

➜ SP - CP = Rs 566.67

Here, we know that, SP - CP = Profit, Hence, Profit is Rs 566.67.

Now,

➜ Profit % = [Profit * 100]/CP

➜ 5 = [566.67 * 100]/CP

➜ CP = [566.67 * 100]/5

➜ CP = 56667/5

➜ CP = Rs 11333.4

Answer : Hence, the cost price is Rs 11333.4.