Question 1

The average weight of 45 passengers in a bus is 52 kg. 5 of them whose average weight is 48 kg leave the bus and other 5 passengers whose average weight is 54 kg join the bus at the same stop. What is the new average weight of the bus?

Accepted Answer

Given total number of passengers in the bus = 45 First average weight of 45 passengers = 52 kgs Average weight of 5 passengers who leave bus = 48 Average weight of 5 passengers who joined the bus = 54 Therefore, the net average weight of the bus is given by = 45 x 52 - 5 x 48 + 5 x 54 45 = 2370 45 = 158 3 = 52 . 66 kgs .

Question 2

19 friends went to a restaurant for a combined weekend dinner party. 13 of them spent Rs. 79 each on their dinner and the rest spent Rs. 4 more than the average expenditure of all the 19. What was the total money spent by them?

Accepted Answer

Let average expenditure was Rs. R 13 x 79 + 6x(R + 4) = 19R => R = Rs. 80.84 Total money = 19 x 80.84 = Rs. 1536.07.

Question 3

If the average height of boys in a hall is 180 cm and that of girls is 150 cm. If the average height of the gathering is 165 cm, then find the number of girls present in the hall if the number of boys present in the hall are 78 ?

Accepted Answer

Using Trial and error method, we get the number of girls in the hall = 78

Question 4

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 ?

Accepted Answer

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.

Question 5

If the mean of a, b, c is M and ab + bc + ca = 0, then the mean of a2+b2+c23 is :

Accepted Answer

We have : ( a + b + c) / 3 = M or (a + b + c) = 3M. Now. a + b + c 2 = 3 M 2 = 9 M 2 . < = > a 2 + b 2 + c 2 + 2 a b + b c + c a = 9 M 2 a 2 + b 2 + c 2 = 9 M 2 , ( a b + b c + c a = 0 ) Required mean = a 2 + b 2 + c 2 3 = 9 M 2 3 = 3 M 2 .

Question 6

In an NGO the daily average wages of 20 illiterate employees is decreased from Rs.25 to Rs.10, thus the average salary of all the literate and illiterate employees is decreased Rs.10 per day. The No. of educated employees working in the NGO is :

Accepted Answer

Total employees = 25 - 10 × 20 10 = 30 Hence number of educated employees = 30-20 = 10

Question 7

A man covers a journey from Meerut to Delhi by a car at an average speed of 40 km/hr. He returns back by scooter with an average speed 24 km/hr. Find his average speed during the whole journey?

Accepted Answer

Since equal distances are covered at 40 kmph and 24 kmph, we can apply the formula 2xy/(x+y) Average speed= (2×40×24)/(40+24) = 30 kmph

Question 8

The average score of boys in an examination in a school is 81 and that of the girls is 83 and the average score of the school is 81.8. Then what will be ratio between the number of girls to the number of boys, in the examination?

Accepted Answer

Let the number of boys = b Let the number of girls = g From the given data, 81b + 83g = 81.8(b + g) 81.8b - 81b = 83g - 81.8g 0.8b = 1.2g b/g = 1.2/0.8 = 12/8 = 3/2 => g : b = 2 : 3 Hence, ratio between the number of girls to the number of boys = 2 : 3.

Question 9

A student's average marks in five subjects is 82. If the average marks of first two subject is 86.5 and the average marks of last two subjects is 84. Find the marks of third subject?

Accepted Answer

The total marks of all 5 subjects = 82 x 5 = 410 Total marks of 1st two subjects = 86.5 x 2 = 173 Total marks of last two subjects = 84 x 2 = 168 Now, marks in 3rd subject = 410 - (173 + 168) = 410 - 341 = 69.

Question 10

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 ?

Accepted Answer

16x + 85 = 17(x + 3) x = 34 + 3 = 37

Question 11

Five boxes of bananas sell for Rs. 30. how many boxes can you buy for Rs.9?

Accepted Answer

Given Five boxes of bananas sell for Rs. 30. => 1 Box of Bananas for = 30/5 = Rs. 6 Then, for Rs. 9 => 9/6 = 3/2 = 1.5 Hence, for Rs. 9, 1.5 box of bananas can buy.

Question 12

Ian has 14 boxes of paper and divides them evenly between 4 coworkers. How many whole boxes did each coworker get?

Accepted Answer

Given number of boxes = 14 Number of workers = 4 Now, number of whole boxes per worker = 14/4 = 3.5 Hence, number of whole boxes per each coworker = 3

Question 13

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 ?

Accepted Answer

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

Question 14

There are 100 students in 3 sections A, B and C of a class. The average marks of all the three sections was 84. The average of B and C was 87.5 and the average marks of students in A section was :

Accepted Answer

Numbers of students in section A = x ∴ Numbers of students in section B and C = (100 – x) ∴ x 70 + (100 – x) 87.5 = 84 100 => 70x + 87.5 100 – 87.5x = 8400 => 8750 – 17.5x = 8400 => 17.5x = 8750 – 8400 => x = 20.

Question 15

Third proportion of 10 and 20 is

Accepted Answer

The third proportional of two numbers p and q is defined to be that number r such that p : q = q : r. Here, required third proportional of 10 & 20, and let it be 'a' => 10 : 20 = 20 : a 10a = 20 x 20 => a = 40 Hence, third proportional of 10 & 20 is 40.

Question 16

Navaneet has thrice the money Poonam has and Poonam has 25% more money than Hebah. If the average money of the three is Rs. 350, What is the amount that Navaneet has ?

Accepted Answer

Assume Hebah has Rs. M Since 25% more money at Poonam => Money at Poonam = M + (25% of M) => Money at Poonam = M + 0.25M = Rs. 1.25M Money with Navaneet is thrice the money with Poonam, => Money at Navaneet = 3(1.25M) = Rs. 3.75M Now, sum of all Money = (M + 1.25M + 3.75M) = Rs. 6M But given the average of the money is Rs. 350 => 6M/3 = 350 => 2M = 350 => M = 350/2 = Rs. 175 => Amount of money Navaneet has = Rs. 3.75M = 3.75 x 175 = Rs. 656.25.

Question 17

The average marks of a student in 7 subjects is 85. His average marks in 6 subjects except English is 83. What is his marks in English ?

Accepted Answer

Marks in English = 85×7 – 83×6 = 595 – 498 = 97

Question 18

Find the average of first 50 natural numbers?

Accepted Answer

We Know that sum of the n natural numbers = n ( n + 1 ) 2 Then sum of 50 natural numbers= 50 ( 51 ) 2 = 1250 Average of the 50 natural numbers = 1250 50 = 25.5

Question 19

The average of five numbers is 27. If one number is excluded, the average becomes 25. The excluded number is :

Accepted Answer

Excluded number = (27 x 5) - (25 x 4) = 135 - 100 = 35.

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