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TCS NQT GuideTCS NQT Numerical AbilityAverages, Mixtures, and Alligations Formulas

Averages, Mixtures, and Alligations Formulas

Learn core concepts, essential formulas, and attempt practice questions designed on the latest TCS NQT testing patterns.

Key Concepts & Formulas

  • 1Average = Sum of observations / Number of observations.
  • 2Weighted Average = (n1 * A1 + n2 * A2) / (n1 + n2).
  • 3Alligation Rule: (Cheaper Qty / Dearer Qty) = (Dearer Price - Mean Price) / (Mean Price - Cheaper Price).

TCS NQT Style Practice Questions

Practice Question 1

In what ratio must rice at Rs. 20/kg be mixed with rice at Rs. 28/kg to get a mixture worth Rs. 25/kg?

A) 3:5
B) 5:3
C) 1:2
D) 2:1

Correct Answer: A) 3:5

Step-by-step Solution: Using alligation rule: Cheaper Price (C) = 20, Dearer Price (D) = 28, Mean Price (M) = 25. Cheaper Qty / Dearer Qty = (D - M)/(M - C) = (28 - 25)/(25 - 20) = 3/5.

Practice Question 2

The average age of 5 students is 20. If a teacher's age is added, the average increases by 2. Find the teacher's age.

A) 32
B) 30
C) 28
D) 35

Correct Answer: A) 32

Step-by-step Solution: Sum of 5 students' age = 5 * 20 = 100. New number of people = 6. New average = 22. New sum = 6 * 22 = 132. Teacher's age = 132 - 100 = 32.

Study Pro-Tip

Alligation is not a separate topic but a graphical methodology for solving complex average mixtures quickly.

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