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Exercise : 4

1. Last year, a Home Appliance Store sold an average(arithmetic mean) of 42 microwave ovens per month. In the first 10 months of this year,the store has sold an average(arithmetic mean) of only 20 microwave ovens per month. What was the average number of microwave ovens sold per month during the entire 22 months period ?

(a) 21

(b) 30

(c) 31

(d) 32

(e) None of the above

**Ans.d**
\(\frac{42 \times 12 + 20 \times 10}{12 + 10} = \frac{504 + 200}{22} = \frac{704}{22} = 32\)
2. The captain of a cricket team of 11 players is 25 years old and the wicket-keeper is 3 years older. If the age of these two players are replaced by that of another two players, the average of the cricket team drops by 2 years. Find the average age of these two players.

(a) 15 years

(b) 15.5 years

(c) 17 years

(d) 16.5 years

(e) None of the above

**Ans.b**
Let average of team = x years

Then, 25 + 28 + S_{9} = 11x … (i)

where S_{9} is the sum of ages of remaining players

Also, Np + S_{9} = 11(x – 2) ,…(ii)

where Np is the sum of ages of new players

(i) – (ii) ⇒ 53 – Np = 22

⇒ Np = 31

∴ Average age of new two players = ^{31}⁄_{2} = 15.5 years

3. A batsman makes a score of 87 runs in the 17th inning and thus increases his average by 3. Find his average after 17th inning.

(a) 36

(b) 39

(c) 42

(d) 45

(e) None of the above

**Ans.b**
Let the average after 17th inning = x.

Then, average after 16th inning = (x – 3).

∴ 16(x – 3) + 87 = 17x or x = (87 – 48) = 39.

4. Nine men went to a hotel. 8 of them spent 3 each over their meals and the ninth spent 2 more than the average expenditure of all the nine. The total money spent by all of them was

(a) 26

(b) 40

(c) 29.25

(d) 27

(e) None of the above

**Ans.c**
Let the average expenditure of all the ninte be x

Then, 3 × 8 + x + 2 = 9x

⇒ x = 3.25

∴ Total money spent = 9x = 9 × 3.25 = 29.25

5. The mean of 30 values was 150. It was detected on rechecking that one value 165 was wrongly copied as 135 for the computation of the mean. Find the correct mean.

(a) 151

(b) 149

(c) 152

(d) 148

(e) None of the above

**Ans.a**
Corrected mean = \(\frac{150 \times 30 - 135 + 165}{30}\)

= \(\frac{4500 - 135 + 165}{30} = \frac{4530}{30} = 151\)

6. A cricketer whose bowling average is 12.4 runs per wicket takes 5 wickets for 26 runs and thereby decreases his average by 0.4. The number of wickets taken by him till the last match was:

(a) 64

(b) 72

(c) 80

(d) 85

(e) None of the above

**Ans.d**
Let the number of wickets taken till the last match be x.

Then,

\(\frac{12.4x + 26}{x + 5}\) = 12 ⇒ 12.4x + 26 = 12x + 60

⇒ 0.4x = 34 ⇒ x = ^{34}⁄_{0.4} = ^{340}⁄_{4} = 85.

7. In an examination, a pupil’s average marks were 63 per paper. If he had obtained 20 more marks for his Geography paper and 2 more marks for his History paper, his average per paper would have been 65. How many papers were there in the examination?

(a) 8

(b) 9

(c) 10

(d) 11

(e) None of the above

**Ans.d**
Let the number of papers be x. Then, 63x + 20 + 2 = 65x

or 2x = 22 or x = 11.

8. A car owner buys petrol at 7.50, 8.00 and 8.50 per litre for three successive years. What approximately is his average cost per litre of petrol if he spends 4000 each year?

(a) 8

(b) 9

(c) 7.98

(d) 8.50

(e) None of the above

**Ans.c**
Let average cost of petrol per litre be x

Then x = \(\frac{12000}{\frac{4000}{7.5} + \frac{4000}{8} + \frac{4000}{8.5}}\)

= \(\frac{3}{\frac{2}{15} + \frac{1}{8} + \frac{2}{17}} = \frac{6120}{767}\) = Rs. 7.98 per litre

9. A batsman has scored an average of 46 runs for a certain number of innings played in England. When he came back to India, he played another two test matches of two innings each and scored at an average of 55 runs. For the innings in England and in India taken together, he has improved his average by 2 runs over the matches played in England.Find the number of innings played in England.

(a) 12

(b) 13

(c) 14

(d) 15

(e) None of these

**Ans.c**
Let the number of innings played in England be x.

∴ Total runs scored in England = 46x

Total runs scored for innings played in India

= 55 × 4 = 220

(∵ the number of innings played in India = 4)

Also, \(\frac{46x + 220}{x + 4}\) = 48

⇒ 46x + 220 = 48 x + 192

⇒ 2x = 28

⇒ x = 14

10. There were 35 students in a hostel. Due to the admission of 7 new students, the expenses of mess were increased by 42 per day while the average expenditure per head diminished by 1. What was the original expenditure of the mess?

(a) 400

(b) 420

(c) 445

(d) 465

(e) None of the above

**Ans.b**
Let the original average expenditure be `x.

Then,

42(x – 1) – 35x = 42 ⇔ 7x = 84 ⇒ x = 12.

∴ Original expenditure = (35 × 12)= 420.