Question

Ram kumar, a trader mixes two varieties of Moong dal, totally weighing 90kg worth Rs7443. The price of the first variety that he mixes is Rs57.50 per kg and that of the second variety is Rs111.50 per kg. How much quantity of the second variety of moong dal does he mix?

• A. 34kg
• B. 38kg
• C. 42kg
• D. 46kg

Hint:

For mixture problems involving different quantities and costs, set up a system of two linear equations: one for the total quantity and another for the total cost. Solve these equations simultaneously to find the unknown quantities.

Answer 1

The Correct Option is C

Let the quantity of the first variety of Moong dal be \( x \) kg.
Let the quantity of the second variety of Moong dal be \( y \) kg.
Step 1: Formulate equations based on given information.
The total weight of the mixture is 90 kg: \[ x + y = 90 \quad \cdots (1) \] The total cost of the mixture is Rs 7443. The price of the first variety is Rs 57.50 per kg, and the second variety is Rs 111.50 per kg: \[ 57.50x + 111.50y = 7443 \quad \cdots (2) \] Step 2: Solve the system of equations.
From equation (1), we can express \( x \) in terms of \( y \): \[ x = 90 - y \] Substitute this expression for \( x \) into equation (2): \[ 57.50(90 - y) + 111.50y = 7443 \] Distribute 57.50: \[ 5175 - 57.50y + 111.50y = 7443 \] Combine the terms with \( y \): \[ 5175 + (111.50 - 57.50)y = 7443 \] \[ 5175 + 54y = 7443 \] Subtract 5175 from both sides: \[ 54y = 7443 - 5175 \] \[ 54y = 2268 \] Divide by 54 to find \( y \): \[ y = \frac{2268}{54} \] \[ y = 42 \] Step 3: Determine the quantity of the second variety.
The quantity of the second variety of moong dal is \( y \).
From the calculation in Step 2, \( y = 42 \) kg.
Therefore, Ram Kumar mixes 42 kg of the second variety of moong dal.