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⁞ Averages

Aptitude ➤ Averages ➤ 1

Average:
Average = Sum of observations / Number of observations

Average Speed :
Suppose a man covers a certain distance at x kmph and an equal distance at y kmph.
Then, the average speed druing the whole journey is [2xy/(x+y)] kmph.

Question 11
Q11.  The average age of husband, wife and their child 3 years ago was 27 years and that of wife and the child 5 years ago was 20 years. The present age of the husband in years is
 

Answer :  40


Sum of the present ages of husband, wife and child = (27 x 3 + 3 x 3) years
= 90 years.
Sum of the present ages of wife and child = (20 x 2 + 5 x 2) years
= 50 years.
Husband's present age = (90 - 50) years
= 40 years
⚔ DISCUSS

Question 12
Q12.  The sum of three consecutive odd numbers is 38 more than the average of these numbers. What is the first of these numbers ?
 

Answer :  17


Let the numbers be x, x+2 and x+4.
Then,

(x + x + 2 + x + 4) -

(x + x + 2 + x + 4)

= 38

3

⇒ (3x + 6) -

(3x + 6)

= 38

3

⇒ 2(3x + 6) = 114
⇒ 6x = 102
⇒ x = 17


⚔ DISCUSS
Question 13
Q13.  A car owner buys petrol at Rs.7.50, Rs. 8 and Rs. 8.50 per litre for three successive years. What approximately is the average cost per litre of petrol if he spends Rs. 4000 each year?
 

Answer :  Rs. 7.98


Total quantity of petrol consumed in 3 years
=(4000/7.50) + (4000/8) + (4000/8.50) litres
= 4000 [ (2/15) + (1/8) + (2/17)]litres
=76700/51 litres

Now , Total amount spent = Rs. (3 x 4000) = Rs. 12000.

∴ Average cost = Rs. (12000 x 51)/76700 = Rs. 6120/767 = Rs. 7.98
⚔ DISCUSS

Question 14
Q14.  The average of six numbers is x and the average of three of these is y. If the average of the remaining three is z, then :
 

Answer :  2x = y + z


Clearly, x = (3y+3z)/6
⇒ 2x= y + z
⚔ DISCUSS

Question 15
Q15.  In Arun's opinion, his weight is greater than 65 kg but less than 72 kg. His brother doest not agree with Arun and he thinks that Arun's weight is greater than 60 kg but less than 70 kg. His mother's view is that his weight cannot be greater than 68 kg. If all of them are correct in their estimation, what is the average of different probable weights of Arun?
 

Answer :  67 Kg


Let Arun's weight be x kg.
According to Arun, 65 < x < 72
According to Arun's brother, 60 < x < 70.
According to Arun's mother, x <= 68

The values satisfying all the above conditions are 66, 67 and 68.
∴ Required average = (66 + 67 + 68)/3 = 201/3 = 67 kg.
⚔ DISCUSS

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