logo

CuriousTab

CuriousTab

Discussion

Home ‣ Aptitude ‣ Alligation or Mixture Comments
  • Question

  • Tea worth of Rs. 135/kg and Rs. 126/kg are mixed with a third variety in the ratio 1: 1 : 2. If the mixture is worth Rs. 153 per kg, the price of the third variety per kg will be____?


  • Options
  • A. Rs. 169.50
  • B. Rs.1700
  • C. Rs. 175.50
  • D. Rs. 180

  • Correct Answer
  • Rs. 175.50 

    Explanation

    To solve the problem, let's define the prices and quantities of the different varieties of tea being mixed.

    Given:

    • Price of the first variety of tea = Rs. 135/kg
    • Price of the second variety of tea = Rs. 126/kg
    • Ratio of the first, second, and third varieties = 1 : 1 : 2

    Let the price of the third variety of tea be x x Rs./kg.

    The total mixture is worth Rs. 153/kg. Since the ratio of the tea varieties is 1:1:2, we can assume the quantities of each type of tea in the mixture to be:

    • Quantity of the first variety = 1 unit
    • Quantity of the second variety = 1 unit
    • Quantity of the third variety = 2 units

    The total cost of the mixture can be expressed as the weighted average cost of the individual varieties based on their respective quantities.

    Let's compute the cost per unit for the mixture:

    Total cost = ( 1  unit × 135  Rs./kg ) + ( 1  unit × 126  Rs./kg ) + ( 2  units × x  Rs./kg ) \text{Total cost} = (1 \text{ unit} \times 135 \text{ Rs./kg}) + (1 \text{ unit} \times 126 \text{ Rs./kg}) + (2 \text{ units} \times x \text{ Rs./kg})

    The total quantity of the mixture is:

    1  unit + 1  unit + 2  units = 4  units 1 \text{ unit} + 1 \text{ unit} + 2 \text{ units} = 4 \text{ units}

    The average price per kg of the mixture is given as Rs. 153. Therefore, we set up the equation:

    135 + 126 + 2 x 4 = 153 \frac{135 + 126 + 2x}{4} = 153

    First, simplify the numerator:

    135 + 126 + 2 x = 261 + 2 x 135 + 126 + 2x = 261 + 2x

    Next, substitute this back into the equation and solve for x x:

    261 + 2 x 4 = 153 \frac{261 + 2x}{4} = 153

    Multiply both sides by 4 to clear the denominator:

    261 + 2 x = 612 261 + 2x = 612

    Now, isolate x x:

    2 x = 612 ? 261 2x = 612 - 261
    2 x = 351 2x = 351
    x = 351 2 x = \frac{351}{2}
    x = 175.5 x = 175.5

    Thus, the price of the third variety of tea is Rs. 175.50 per kg.

    • Tags: CAT, Bank Exams, AIEEE

    Alligation or Mixture problems

    Search Results

    • 1. A vessel is filled with liquid, 3 parts of which are water and 5 parts of syrup. How much of the mixture must be drawn off and replaced with water so that the mixture may be half water and half syrup?

    • Options
    • A. 1/3
    • B. 1/4
    • C. 1/5
    • D. 1/7
      • Discuss
    • 2. In what proportion water must be added to spirit to gain 20% by selling it at the cost price?

    • Options
    • A. 1:5
    • B. 1:6
    • C. 1:7
    • D. 1:8
      • Discuss
    • 3. The ratio of expenditure and savings is 3 : 2 . If the income increases by 15% and the savings increases by 6% , then by how much percent should his expenditure increases?

    • Options
    • A. 25
    • B. 21
    • C. 12
    • D. 24
      • Discuss
    • 4. A mixture of 150 liters of wine and water contains 20% water. How much more water should be added so that water becomes 25% of the new mixture?

    • Options
    • A. 10 liters
    • B. 20 liters
    • C. 30 liters
    • D. 40 liters
      • Discuss
    • 5. How many kilograms of sugar costing Rs. 9 per kg must be mixed with 27 kg of sugar costing Rs. 7 per Kg so that there may be a gain of 10 % by selling the mixture at Rs. 9.24 per Kg?

    • Options
    • A. 36 Kg
    • B. 42 Kg
    • C. 54 Kg
    • D. 63 Kg
      • Discuss

    Comments

    There are no comments.
Enter a new Comment




Aptitude

Engineering

Programming

Reasoning

Links

Copyright ©CuriousTab. All rights reserved.