• Averages, Mixtures and Alligation Aptitude basics, practice questions, answers and explanations 
  Prepare for companies tests and interviews
   

• Average= (x₁+x₂+x₃+......x_n)/n
   where x₁,x₂,x₃, are quantities.
•  
• Weighted Average= (n₁x₁+n₂x₂+n₃x₃+.....n_kx_k) / n₁+n₂+n₃+......n_k
   where x₁,x₂,x₃.... x_k are the quality factors
  n₁,n₂,n₃,........n_k are the quantity factors
  
  

  Eg: If the average height of boys= 172cms and that of girls=154 cms, then find average height of the class with 18 boys and 12 girls?

• 
  Here n₁ and n₂ are no. of boys and girls (Quantity factor)
  x₁ and x₂ are average heights (Quality factor)

•  

• Mixtures
  For mixtures, Average, x'= (n₁x₁+n₂x_{2)/ (}n₁+n₂)
                                                         

• Alligation:
  
  
   

=> n₁/n₂ = (x₂-x')/x'-x₁
   

Exercise questions

 

1. The average wages of a worker during a fortnight comprising 15 consecutive working days was Rs.90 per day. During the first 7 days, his average wages was Rs.87/day and the average wages during the last 7 days was Rs.92 /day. What was his wage on the 8th day?

a)83   
b) 92           

c)90             

d)97

2. The average of 5 quantities is 6. The average of 3 of them is 8. What is the average of the remaining two numbers?

a) 6.5      b) 4              c) 3               d) 3.5

3. The average temperature on Wednesday, Thursday and Friday was 250. The average temperature on Thursday, Friday and Saturday was 240. If the temperature on Saturday was 270, what was the temperature on Wednesday?

a) 240    
b)210        

c) 270             

d) 300

4. The average age of a group of 12 students is 20years. If 4 more students join the group, the average age increases by 1 year. The average age of the new students is

a) 24               

b)26               

c)23               

d) 22

5. When a student weighing 45 kgs left a class, the average weight of the remaining 59 students increased by 200g. What is the average weight of the remaining 59 students?

a) 57 kgs            

b) 56.8 kgs      

c)58.2 kgs  

d)52.2 kgs

6. The average of 5 quantities is 10 and the average of 3 of them is 9. What is the average of the remaining 2?

a) 11      

b) 12            

c) 11.5          

d) 12.5

7. The average age of a family of 5 members is 20 years. If the age of the youngest member be 10 years then what was the average age of the family at the time of the birth of the youngest member?

a) 13.5                

b) 14             

c)15                

d) 12.5

8. Average cost of 5 apples and 4 mangoes is Rs.36. The average cost of 7 apples and 8 mangoes is Rs.48. Find the total cost of 24 apples and 24 mangoes.

a) Rs.1044             

b) RS.2088          

c)Rs.720  

d) Rs.324

9. Tea worth Rs. 126 per kg and Rs. 135 per 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:

a) Rs. 169.50              
b) Rs. 170     
c) Rs. 175.50            
d) Rs. 18

10. A vessel is filled with liquid, 3 parts of which are water and 5 parts 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?

a) 1/3              

b) 1/4                
c) 1/5              
d) 1/7

Answer Key

1.d; 2.c; 3.d; 4.a; 5.a; 6.c; 7.d; 8.b; 9.c; 10.c