Two-price currants blended to a target price: Currants at ₹ 50/kg are mixed with currants at ₹ 90/kg to make 17 kg of mixture worth ₹ 70/kg. How many kilograms of each type are used?

Introduction / Context: This is a direct weighted average. Let x be the mass at ₹ 50/kg, then (17 − x) is at ₹ 90/kg. Enforce the total value equal to 17 * ₹ 70, and solve x. The solution reveals whether the mix is equal or skewed to either side.

Given Data / Assumptions:

• Total mass = 17 kg; target price = ₹ 70/kg ⇒ total value = ₹ 1190.
• Costs: ₹ 50/kg and ₹ 90/kg.
• Unknowns: x kg at ₹ 50/kg; 17 − x kg at ₹ 90/kg.

Concept / Approach: Equation: 50x + 90(17 − x) = 1190. Solve for x. The complementary mass is 17 − x.

Step-by-Step Solution:

Verification / Alternative check: Value = 8.5*50 + 8.5*90 = 425 + 765 = 1190; average = 1190/17 = ₹ 70/kg, correct.

Why Other Options Are Wrong: Other splits do not yield ₹ 1190 total value at 17 kg; the average would shift away from ₹ 70/kg.

Common Pitfalls: Using ratio 50:90 directly on masses without enforcing the 17-kg total and the ₹ 70/kg target average.

Final Answer: 8 1/2 kg of each