A trader sells two types of nuts. Type A is sold at a profit of \rupee 8 per kg and Type B at a loss of \rupee 5 per kg. He sells a total of 50 kg of nuts and his overall profit is \rupee 140. How many kilograms of each type did he sell?

hard 5 marks Class 10 · Mathematics · Pair of Linear Equations in Two Variables

Answer

He sold 30 kg of Type A and 20 kg of Type B.

The correct answer is He sold 30 kg of Type A and 20 kg of Type B. — Find $y$ using $y = 50 - x$ : $y = 50 - 30 = 20$ .

Step-by-step solution

Let $x$ be the kilograms of Type A and $y$ the kilograms of Type B.
Write the total weight equation: $x + y = 50$ .
Write the profit equation (profit $=$ profit per kg $\times$ kg): $8 x - 5 y = 140$ .
From the first equation, express $y = 50 - x$ .
Substitute $y$ in the profit equation: $8 x - 5 (50 - x) = 140$ .
Simplify: $8 x - 250 + 5 x = 140 \Rightarrow 13 x = 390 \Rightarrow x = 30$ .
Find $y$ using $y = 50 - x$ : $y = 50 - 30 = 20$ .

Common mistake: Treating the loss as a positive contribution instead of a negative one

Concept tested: Solving word problems with profit and loss