MATHS (SOLVED IN STEPS) Problems on Average - (Page -3)

15. A batsman makes a score of 87 runs in the 17^th inning and thus increases his averages by 3. What is his average after 17th inning?

A. 39 B. 35 C. 42 D. 40.5

Answer : Option A

Explanation :

Let the average after 17 innings = x

Total runs scored in 17 innings = 17x

then average after 16 innings = (x-3)

Total runs scored in 16 innings = 16(x-3)

We know that Total runs scored in 16 innings + 87

= Total runs scored in 17 innings

= > 16(x-3) + 87 = 17x

= > 16x - 48 + 87 = 17x

= > x = 39

16. There are two divisions A and B of a class, consisting of 36 and 44 students respectively. If the average weight of divisions A is 40 kg and that of division b is 35 kg. What is the average weight of the whole class?

A. 38.25 B. 37.25 C. 38.5 D. 37

Answer : Option B

Explanation:

Total weight of students in division A = 36×40

Total weight of students in division B = 44×35

Total students = 36+44=80

Average weight of the whole class= {(36×40)+(44×35)}/80

= {(9×40)+(11×35)}/20

= {(9×8)+(11×7)}/4

= (72+77)/4

= 149/4=37.25

17. A student needed to find the arithmetic mean of the numbers 3, 11, 7, 9, 15, 13, 8, 19, 17, 21, 14 and x. He found the mean to be 12. What is the value of x?

A. 12 B. 5 C. 7 D. 9

Answer : Option C

Explanation :

(3+11+7+9+15+13+8+19+17+21+14+x)/12=12

= > (137+x)/12=12

= > 137 + x = 144

= > x = 144 - 137 = 7

18. Arun obtained 76, 65, 82, 67 and 85 marks (out in 100) in English, Mathematics, Chemistry, Biology and Physics. What is his average mark?

A. 53 B. 54 C. 72 D 75

Answer : Option D

Explanation :

Average mark = (76+65+82+67+85)/5=375#5=75

19. Distance between two stations A and B is 778 km. A train covers the journey from A to B at 84 km per hour and returns back to A with a uniform speed of 56km per hour. Find the average speed of the train during the whole journey?

A. 69.0 km /hr B. 69.2 km /hr C. 67.2 km /hr D. 67.0 km /hr

Answer : Option C

Explanation :

If a car covers a certain distance at x kmph and an equal distance at y kmph.

Then,the average speed of the whole journey = 2xy/x+y kmph.By using the same formula, we can find out the average speed quicklyaverage speed = 2×84×56# (84+56) = (2×84×56)#140==67.2

20. The average age of 36 students in a group is 14 years. When teacher’s age is included to it, the average increases by one. Find out the teacher’s

age in years?

A. 51 years, B. 49 years C. 53 years D. 50 years

Answer : Option A

Explanation :

average age of 36 students in a group is 14

= > Sum of the ages of 36 students = 36×14

When teacher’s age is included to it, the average increases by one => average = 15

= > Sum of the ages of 36 students and the teacher =37×15

Hence teachers age = 37×15"36×14=37×15"14(37"1)=37×15"37×14+14=37(15"14)+14=37+14=51

21. The average of five numbers id 27. If one number is excluded, the average becomes 25. What is the excluded number?

A. 30, B. 40, C. 32.5, D. 35