Given:
Buying a carriage with a horse for Rs 4000 makes a profit of 3.5% if the horse is sold at a profit of 20% and the carriage at a loss of 10%.
Concept:
To find the cost price of the horse, we need to set up equations based on the given profit and loss percentages and solve them.
Formula Used:
Profit Percentage = (Profit / Cost Price) × 100
Loss Percentage = (Loss / Cost Price) × 100
Calculation:
Let the cost price of the horse be Rs H and the cost price of the carriage be Rs C.
Given, H + C = 4000
Horse is sold at a profit of 20%:
⇒ Selling Price of Horse = H + 0.20H = 1.20H
Carriage is sold at a loss of 10%:
⇒ Selling Price of Carriage = C - 0.10C = 0.90C
Total Selling Price = 1.20H + 0.90C
Given, the total profit is 3.5%:
⇒ Total Selling Price = 4000 + 0.035 × 4000 = 4000 + 140 = 4140
We have the equation:
1.20H + 0.90C = 4140
We also have H + C = 4000
Solving these two equations:
From H + C = 4000, we get C = 4000 - H
Substitute C in the first equation:
⇒ 1.20H + 0.90(4000 - H) = 4140
⇒ 1.20H + 3600 - 0.90H = 4140
⇒ 0.30H = 540
⇒ H = 540 / 0.30
⇒ H = 1800
Hence, the cost price of the horse is Rs 1800.
∴ The correct answer is option 4.