Exercise : 5


1. A family consists of grandparents, parents and three grand children. The average age of the grandparents is 67 years, that of the parents is 35 years and that of the grandchildren is 6 years. What is the average age of the family?
(a) 2847 years
(b) 3157 years
(c) 3217 years
(d) 2712 years
(e) None of these
Ans.b

Required average = \(\left ( \frac{67 \times 2 + 35 \times 2 + 6 \times 3}{2 + 2 + 3} \right )\)

= \(\left ( \frac{134 + 70 + 18}{7} \right ) = \frac{222}{7}\)

= 3157 years

2. In Arun’s opinion, his weight is greater than 65 kg but less than 72 kg. His brother does 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?
(a) 67 kg
(b) 68 kg
(c) 69 kg
(d) 66.5 kg
(e) None of the above
Ans.d

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 and 67.

∴ Required average = \(\left ( \frac{66 + 67}{2} \right ) = \left ( \frac{133}{2} \right ) = 66.5 \; kg.\)

3. The average age of a board of 8 functional directors in a company is the same as it was 3 years ago, a younger man having been substituted for one of the directors. How much younger was the new man than the director whose place he took.
(a) 24 years
(b) 26 years
(c) 28 years
(d) 27 years
(e) None of the above
Ans.a

Let the new man was younger than the director = x years and 3 years ago, the sum of ages of board of directors

= S – 8 × 3 = S – 24

Then, 3 years ago, average age of board of directors

= \(\frac{S - 24}{8}\)

Now, \(\frac{S - 24}{8} = \frac{S - x}{8}\)

⇒ x = 24 years

Shortcut Method : If the new young director would have been not substituted, then total age would have increased at present by 8 × 3 = 24 years.

Therefore, the new man is 24 years younger keeping the average at present same as 3 years ago.

4. A batsman makes a scores of 98 runs in his 19th inning and thus increases his average by 4. What is his average after 19th inning ?
(a) 22
(b) 24
(c) 28
(d) 26
(e) None of the above
Ans.d

Let the average score of 19 innings be x.

Then, \(\frac{18x + 98}{19} = x + 4\)

The average score after 20th innings

= x + 4 = 22 + 4 = 26

5. The average weight of 45 students in a class is 52 kg. 5 of them whose average weight is 48 kg leave the class and other 5 students whose average weight is 54 kg join the class. What is the new average weight (in kg) of the class ?
(a) 5113
(b) 5223
(c) 5213
(d) 43.42
(e) None of these
Ans.b

Total weight of 45 students

= 45 × 52 = 2340 kg

Total weight of 5 students who leave

= 5 × 48 = 240 kg

Total weight of 5 students who join

= 5 × 54 = 270 kg

Therefore, new total weight of 45 students

= 2340 – 240 + 270 = 2370

⇒ New average weight = 237045 = 5223 kg

6. The average of 10 numbers is 40.2. Later it is found that two numbers have been wrongly copied. The first is 18 greater than the actual number and the second number added is 13 instead of 31. Find the correct average.
(a) 40.2
(b) 40.4
(c) 40.6
(d) 40.8
(e) None of the above
Ans.a

Sum of 10 numbers = 402

Corrected sum of 10 numbers

= 402 – 13 + 31 – 18 = 402

Hence, new average = 40210 = 40.2