A man purchases a bullock and a cart together for Rs. 1,800. He sells the bullock at a profit of 20% and the cart at a profit of 30%. His overall profit on the combined sale is 155/6%. What was the cost price of the bullock?

Introduction / Context:
This problem combines percentage profit on individual items with an overall percentage profit on their combined cost price. The man buys a bullock and a cart together, sells each at different profit rates, and is given the overall profit percentage. We are asked to find the cost price of just the bullock. This type of question is commonly used to test algebraic modeling of word problems in profit and loss.

Given Data / Assumptions:

• Total cost price of bullock and cart together = Rs. 1,800.
• Bullock is sold at a profit of 20%.
• Cart is sold at a profit of 30%.
• Overall profit on the combined transaction = 155/6%.
• Let cost price of bullock be x and cost price of cart be 1800 − x.

Concept / Approach:
We use profit percentage formulas and write expressions for selling prices based on cost prices. Bullock selling price is 1.20 times its cost; cart selling price is 1.30 times its cost. The overall selling price for both items combined is then calculated using the overall profit percentage. Equating the sum of individual selling prices to the overall selling price expression gives a linear equation in x, which we solve to find the cost price of the bullock.

Step-by-Step Solution:
Let the cost price of the bullock be x.Then the cost price of the cart is 1800 − x.Bullock is sold at a 20% profit, so its selling price = 1.20 * x.Cart is sold at a 30% profit, so its selling price = 1.30 * (1800 − x).Overall cost = 1800.Overall profit percentage = 155/6% = 155 / 600 as a decimal ≈ 0.2583.Overall selling price = 1800 * (1 + 155/600) = 1800 * (755/600).Compute: 1800 * (755/600) = 3 * 755 = Rs. 2,265.So, 1.20x + 1.30(1800 − x) = 2265.Expand: 1.20x + 2340 − 1.30x = 2265.Combine like terms: (1.20 − 1.30)x + 2340 = 2265 ⇒ −0.10x + 2340 = 2265.So −0.10x = 2265 − 2340 = −75 ⇒ x = 750.Therefore, the cost price of the bullock is Rs. 750.

Verification / Alternative check:
Bullock cost = 750, selling price = 1.20 * 750 = Rs. 900.Cart cost = 1800 − 750 = 1050, selling price = 1.30 * 1050 = Rs. 1,365.Total cost = 750 + 1050 = 1800; total selling price = 900 + 1365 = 2265.Overall profit = 2265 − 1800 = 465.Profit percentage = (465 / 1800) * 100 = 25.833...%, which equals 155/6%, matching the question.

Why Other Options Are Wrong:
If bullock cost were Rs. 650 or Rs. 800 or Rs. 900, recomputing selling prices would not give overall profit of 155/6%.Only Rs. 750 as the bullock cost price satisfies both the individual profit conditions and the overall profit condition.

Common Pitfalls:
Misreading 155/6% as 155.6% instead of 155 divided by 6 is a common error.Some learners incorrectly assume equal cost division between bullock and cart instead of using variables.Others forget that the overall profit applies to the total cost, not separately to each item.

Final Answer:
The cost price of the bullock was Rs. 750.