Question

QueSLUIT IU
A dealer bought a car at Rs. 12.5 lakh and marked it at 18 lakh. He offered a discount
and then sold it. His profit /loss percentage and discount percentage are in the ratio
6:5. Find his profit/loss percentage.​

Answer 1

Let the cost price be Rs. x

In the loss process,

Cost price = Rs. x lakhs

Selling price = Rs. 7.6 lakhs

Loss = Cost price – Selling price = x – 7.6

In the profit process,

Cost price = Rs. x lakhs

Selling price = Rs. 9.2 lakhs

Profit = Selling price – Cost price = 9.2 – x

Given that profit = 3 × loss ⇒ 9.2 – x = 3(x – 7.6)

⇒ x = 8

∴ Cost price = Rs. 8 lakhs.

Answer 2

Given :-

• CP of car = Rs. 12.5 lakh
• MP of car = Rs. 18 lakh
• Profit/Loss % : Discount % = 6 : 5

To Find :- Find his profit/loss percentage.

Solution :-

Case (1) :- Profit % : Discount % = 6 : 5

Let SP of car is equal to Rs. x .

So,

→ Profit = SP - CP = Rs.(x - 12,50,000)

→ Profit % = (Profit × 100) / CP = {(x - 1250000) * 100}/1250000 = {(x - 1250000)/12500} % -------- Equation (1)

and,

→ Discount = MP - SP = Rs. (1800000 - x)

→ Discount % = (Discount × 100)/MP = {(1800000 - x) * 100} / 1800000 = {(1800000 - x)/18000}

A/q,

→ Profit % / Discount % = 6/5

→ {(x - 1250000)/12500} / {(1800000 - x)/18000} = 6/5

→ 18000(x - 1250000) / 12500(1800000 - x) = 6/5

→ 30(x - 1250000) = 25(1800000 - x)

→ 6(x - 1250000) = 5(1800000 - x)

→ 6x - 7500000 = 9000000 - 5x

→ 6x + 5x = 9000000 + 7500000

→ 11x = 16500000

→ x = Rs.1500000

therefore, putting value of x in Equation (1),

→ Profit % = {(x - 1250000)/12500} = (1500000 - 1250000) / 12500 = 250000/12500 = 20% (Ans.)

Case 2) :- Loss % : Discount % = 6 : 5

Let SP of car is equal to Rs. x .

So,

→ Loss = CP - SP = Rs.(12,50,000 - x)

→ Loss % = (Loss × 100) / CP = {(1250000 - x) * 100}/1250000 = {(1250000 - x)/12500} % -------- Equation (2)

and,

→ Discount = MP - SP = Rs. (1800000 - x)

→ Discount % = (Discount × 100)/MP = {(1800000 - x) * 100} / 1800000 = {(1800000 - x)/18000}

A/q,

→ Loss % / Discount % = 6/5

→ {(1250000 - x)/12500} / {(1800000 - x)/18000} = 6/5

→ 18000(1250000 - x) / 12500(1800000 - x) = 6/5

→ 30(1250000 - x) = 25(1800000 - x)

→ 6(1250000 - x) = 5(1800000 - x)

→ 7500000 - 6x = 9000000 - 5x

→ (-6x) + 5x = 9000000 - 7500000

→ (-x) = 1500000

→ x = (-1500000)

since value of x is negative here . This case is not possible .

Hence, Profit percentage of dealer is equal to 20% .

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