169+ Problems on Average With Explanation

Q:

Out of 9 persons, 8 persons spent Rs. 30 each for their meals. The ninth one spent Rs. 20 more than the average expenditure of all the nine. The total money spent by all of them was :

A) Rs. 292.50	B) Rs. 297.50
C) Rs. 298	D) Rs. 298.50

Answer & Explanation Answer: A) Rs. 292.50

Explanation:

Let the average expenditure be Rs. x Then,

9x=[(8*30)+(x+20)]<=>9x =x+260 <=> x =32.50

Total money spent = 9x = Rs. (9 x 32.5O) = Rs 292. 50

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Q:

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. What is the teacher's age in years ?

A) 35 years	B) 45 years
C) 51 years	D) 54 years

Answer & Explanation Answer: C) 51 years

Explanation:

Age of the teacher = (37 * 15 - 36 * 14) years = 51 years.

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Q:

A batsman in his 17th innings makes a score of 85 and their by increasing his average by 3. What is his average after the 17th innings ?

A) 34	B) 36
C) 35	D) 37

Answer & Explanation Answer: D) 37

Explanation:

16x + 85 = 17(x + 3)

x = 34 + 3 = 37

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Q:

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

Answer & Explanation Answer: D) 11

Explanation:

Let the number of papers be x. Then, 63x + 20 + 2 = 65x or 2x = 22 or x = 11.

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Q:

A student was asked 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 should be the number in place of x ?

A) 6	B) 7
C) 8	D) 9

Answer & Explanation Answer: B) 7

Explanation:

Clearly, we have (3 + 11 + 7 + 9 + 15 + 13 + 8 + 19 + 17 + 21 + 14 + x) / 12 = 12.

or 137 + x = 144 or x = 144 - 137 = 7.

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Q:

A family consists of grandparents, parents and three grandchildren. 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) 31( 5/7)	B) 32 (6/7)
C) 34(4/7)	D) 35(4/9)

Answer & Explanation Answer: A) 31( 5/7)

Explanation:

Required average = (67 * 2 + 35 * 2 + 6 * 3) / (2 + 2 + 3)

= (134 + 70 + 18) / 7 = 222 / 7 = 31(5/7) years.

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Q:

The average price of 10 books is Rs. 12 while the average price of 8 of these books is Rs. 11.75. Of the remaining two books, if the price of one book is 60% more than the price of the other, what ia the pice of each of these two books ?

A) 16,12	B) 10,16
C) 23,9	D) 8,7

Answer & Explanation Answer: B) 10,16

Explanation:

Total pice of the two books = Rs. [(12 x 10) - (11.75 x 8)]

= Rs. (120 - 94) = Rs. 26.

let the price of one book be Rs. x

Then, the price of other book = Rs. (x + 60% of x) = Rs.(x+(3/5)x) = Rs. (8/5)x

So, x+(8/5)x =26 <=> x =10

The prices of the two books are Rs. 10 and Rs. 16

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Q:

The average of six numbers is 3.95. The average of two of them is 3.4, while the average of the other two is 3.85. What is the average of the remaining two numbers ?

A) 3.6	B) 4.6
C) 6.5	D) 7.3

Answer & Explanation Answer: B) 4.6

Explanation:

Sum of the remaining two numbers = (3.95 * 6) - [(3.4 * 2) + (3.85 * 2)]

= 23.70 - (6.8 + 7.7) = 23.70 - 14.5 = 9.20.

Required average = (9.2 / 2) = 4.6.

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