Question 1

A certain factory employed 600 men and 400 women and the average wager was Rs. 25.50 per day, If a woman got Rs. 5 less than a man, then what are their daily wages ?

Accepted Answer

Let the daily wage of a man be Rs. x. Then, daily wage of a woman = Rs. (x - 5). Now, 600x + 400 (x - 5) = 25.50 * (600 + 400) <=> 1000x = 27500 <=> x = 27.50. Man's daily wages = Rs. 27.50; Woman's daily wages = (x - 5) = Rs. 22.50.

Question 2

The average age of students of a class is 15.8 years. The average age of boys in the class is 16.4 years and that of the girls is 15.4 years, The ratio of the number of boys to the number of girls in the class is :

Accepted Answer

Let the ratio be k : 1. Then, k * 16.4 + 1 * 15.4 = (k + 1) * 15.8 <=> (16.4 - 15.8) k = (15.8 - 15.4) <=> k = 0.4/0.6 = 2/3. Required ratio = 2/3 : 1 = 2 : 3.

Question 3

The average temperature for Monday, Tuesday, Wednesday and Thursday was 48 degrees and for Tuesday, Wednesday, Thursday and Friday was 46 degrees. If the temperature on Monday was 42 degrees. Find the temperature on Friday ?

Accepted Answer

M + Tu + W + Th = 4 x 48 = 192 Tu + W + Th + F = 4 x 46 = 184 M = 42 Tu + W + Th = 192 - 42 = 150 F = 184 – 150 = 34

Question 4

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 ?

Accepted Answer

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.

Question 5

A library has an average of 510 visitors on Sundays and 240 on other days. The average number of visitors per day in a month of 30 days beginning with a Sunday is :

Accepted Answer

Since the month begins with a Sunday, so there will be five Sundays in the month, Required average = (510 * 5 + 240 * 25) / 30 = 8550/30 = 285.

Question 6

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 7

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 8

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 9

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 10

12 boys decided to constribute Rs. 750 each to an Orphange. Suddenly few of them boys dropped out and consequently the rest had to pay Rs. 150 more. Then the number of boys who dropped out?

Accepted Answer

Total money decided to contribute = 750 x 12 = 9000 Let 'b' boys dropped The rest paid 150/- more => (12 - b) x 900 = 9000 => b = 2 Hence, the number of boys who dropped out is 2.

Question 11

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 12

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 13

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 14

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 15

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 16

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 17

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 18

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 19

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

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