SSC CGL Tier I 13 Sep 2025 Shift 2 Paper

Concept:The cost price of a mixture is the weighted average of the costs of its components. When sold at a profit, selling price equals cost price multiplied by (1 + profit percentage). We first find the mixture’s cost price using the given selling price and profit.Explanation:Let the price of the third variety be $x$ per kg. The pulses are mixed in the ratio 1 : 1 : 2, so the total weight in the mixture corresponds to 4 parts.Selling price of the mixture is $72$ per kg, and profit is 20%. So, cost price (CP) of the mixture is:$$CP = \frac{SP}{1 + \text{profit\%}} = \frac{72}{1.20} = 60 \text{ per kg}$$Now, the weighted average cost of the mixture equals this CP:$$\frac{1 \times 50 + 1 \times 60 + 2 \times x}{1+1+2} = 60$$Simplify numerator: $50 + 60 + 2x = 110 + 2x$. Denominator is 4. Hence:$$\frac{110 + 2x}{4} = 60$$Multiply both sides by 4: $110 + 2x = 240$. Subtract 110: $2x = 130$. Divide by 2: $x = 65$.Answer:The price of the third variety of pulse is $65$ per kg, which corresponds to option A.