Question 1

The average age of 15 students of a class is 15 years. Out of these, the average age of 5 students is 14 years and that of the other 9 students is 16 years, The age of the 15th student is :

Accepted Answer

Age of the 15th student = [15 * 15 - (14 * 5 + 16 * 9)] = (225-214) = 11 years.

Question 2

The ratio of speeds of a car, a train and a bus is 5:9:4. The average speed of the car, the bus and the train is 72 km/hr together. What is the average speed of the car and the train together ?

Accepted Answer

Let the speeds of the car, train and bus be 5x, 9x and 4x km/hr respectively. Average speed = 5x + 9x + 4x/3 = 18x /3 = 6x km/hr. Also, 6x = 72 => x = 12 km/hr Therefore, the average speed of the car and train together is = 5 x + 9 x 2 = 7x = 7 x 12 = 84 km/hr.

Question 3

Out of three numbers, the first is twice the second and is half of the third. If the average of the three numbers is 56, what will be the sum of the highest number and the lowest number?

Accepted Answer

Let the three numbers be x, y, z. From the gien data, x = 2y ....(1) x = z/2 => z = 2(2y) = 4y .....(From 1) ...........(2) Given average of three numbers = 56 Then, x + y + z 3 = 56 2 y + y + 4 y 3 = 56 ( From 1 & 2 ) 7 y = 56 x 3 y = 24 Now, x = 2y => x = 2 x 24 = 48 z = 4y = 4 x 24 = 96 Now, the highest number is z = 96 & smallest number is y = 24 Hence, required sum of highest number and smallest number = z + y = 96 + 24 = 120.

Question 4

The average monthly salary of 20 employees in an organisation is Rs. 1500. If the manager's salary is added, then the average salary increases by Rs. 100. What is the manager's monthly salary ?

Accepted Answer

Manager's monthly salary Rs. (1600 * 21 - 1500 * 20) = Rs. 3600.

Question 5

After replacing an old member by a new member, it was found that the average age of five members of a club is the same as it was 3 years ago. The difference between the ages of the replaced and the new members?

Accepted Answer

Let avg ages of 5 members at present is G And age of new member is m and an older is n Required = (5G + m - n)/5 = G - 3 m - n = 15 years

Question 6

In a mixture of three varities of oils , the ratio of their weight is 4 : 5 : 8. If 5 kg of oils of the first variety, 10 kg of the second variety and some quantity of oils of the third variety are added to the mixture, the ratio of the weights of t…

Accepted Answer

Let the ratio of initial quantity of oils be 'x' => 4x, 5x & 8x. Let k be the quantity of third variety of oil in the final mixture. Let the ratio of initial quantity of oils be 'y' From given details, 4x + 5 = 5y ..... (1) 5x + 10 = 7y .....(2) 8x + k = 9y ......(3) By solving (1) & (2), we get x = 5 & y = 5 From (3) => k = 5 Therefore, quantity of third variety of oil was 9y = 9(5) = 45kg.

Question 7

What will be the cost of building a fence around a square plot with area equal to 289 sq ft, if the price per foot of building the fence is Rs. 58 ?

Accepted Answer

Let the side of the square plot be 'a' ft. Given area of the plot (a x a) = 289 => a = 17 Length of the fence = Perimeter of the plot = 4a = 68 ft. Cost of building the fence = 68 x 58 = Rs. 3944.

Question 8

It costs Rs. p each to send the first thousand messsages and Rs. q to send each subsequent one . If r is greater than 1,000, how many Rupees will it cost to send r messages ?

Accepted Answer

We need to find the total cost to send r messsages, r > 1000. The first 1000 messsages will cost Rs.p each (Or) The total cost of first 1000 messsages = Rs.1000p The remaining (r - 1000) messsages will cost Rs.q each (Or) The cost of the (r - 1000) = Rs.(r - 1000)y Therefore, total cost = 1000p + rq - 1000q = 1000(p - q) + qr

Question 9

Three maths classes: A, B and C take an algebra test. The average score of class A is 83. The average score of class B is 76. The average score of class C is 85. The average score of class A and B is 79 and average score of class B and C is 81. What…

Accepted Answer

Let the number of students in classes A, B and C be P, Q and R respectively. Then, total score of A = 83P, total score of B = 76Q, total score of C = 85R. Also given that, (83P + 76Q) / (P + Q) = 79 =>4P = 3Q. (76Q + 85R)/(Q + R) = 81 =>4R = 5Q, =>Q = 4P/3 and R = 5P/3 Therefore, average score of A, B, C = ( 83P + 76Q + 85R ) / (P + Q + R) = 978/12 = 81.5

Question 10

The average of marks in 3 subjects is 224. The first subject marks is twice the second and the second subject marks is twice the third. Find the second subject marks ?

Accepted Answer

Let the third subject marks be 'x' => Second subject marks = 2x => Third subject marks = 4x Given avg = 224 x + 2x + 4x = 224 x 3 => 7x = 224 x 3 => x = 96 Hence, Second subject marks = 2x = 2 x 96 = 192.

Question 11

How many window coverings are necessary to span 50 windows, if each window covering is 15 windows long?

Accepted Answer

Given that, Number of windows = 50 Each window covering covers 15 windows => 50 windows requires 50/15 window coverings = 50/15 = 3.333 Hence, more than 3 window coverings are required. In the options 4 is more than 3. Hence, 4 window coverings are required to cover 50 windows of each covering covers 15 windows.

Question 12

16 children are to be divided into two groups A and B of 10 and 6 children. The average percent marks obtained by the children of group A is 75 and the average percent marks of all the 16 children is 76. What is the average percent marks of children…

Accepted Answer

Required average = [(76 * 16) - (75 * 10)] / 6 = (1216 - 750)/6 = 466/3 = 233 /3.

Question 13

The average age of the boys in a class is 16 years and that of the girls is 15 years. The average age for the whole class is :

Accepted Answer

Clearly, to find the average, we ought to know the number of boys, girls or students in the class, neither of which has been given. So, the data provided is inadequate.

Question 14

What is the average of four tenths and five thousandths

Accepted Answer

Four tenths = 0.4 Five thousandths = 0.005 The average is (0.4 + 0.005)/2 = 0.2025

Question 15

The average of any 5 consecutive odd natural numbers is k . If two more such numbers , just next to the previous 5 numbers are added , the new average becomes

Accepted Answer

The 5 consecutive odd numbers whose average is k are (k-4), (k-2), k, (k+2), (k+4) Again the average of (k-4), (k-2), k, (k+2), (k+4), (k+6), (k+8) is (k+2)

Question 16

The average of six numbers is x and the average of three of these is y. If the average of the remaining three is z, then :

Accepted Answer

Clearly, we have : x = (3y + 3z ) / 6 or 2x = y + z.

Question 17

In a village the average age of n people is 42 years. But after the verification it was found that the age of a person had been considered 20 years less than the actual age, so the new average, after the correction,increased by 1. The value of n is :

Accepted Answer

It is the same as a person with 20 years more age replaces an existing person of the group ( or village) Since the total age of the village having n persons, is being increased by 20 years and the average age of village is being increased by 1 year, hence there are total 20 people in the village. Alternatively : ( n x 42 ) + 20 = ( n x 43 ) => n=20

Question 18

The average expenditure of the hotel when there are 10 guests is Rs. 60 per guests and the average expenditure is Rs.40 when there are 20 Guests. If it is known that there are some fixed expenses irrespective of the number of guests then the average…

Accepted Answer

Let the fixed expenditure of the hotel be Rs.x and the variable expenditure ( which is dependent on the guest ) is Rs.y , then x + 10y = 600 ---------(1) x + 20y = 800 ----------(2) From (1) & (2) 10y = 200 => y = Rs. 20 and x= 400 Hence the total expenditure when there are 40 guests = 400 + 40 x 20 = 1200 Therefore, average expenditure = 1200/40 = Rs. 30

Question 19

There are 44 students in a hostel, due to the administration, 15 new students has joined. The expense of the mess increase by Rs. 33 per day. While the average expenditure per head diminished by Rs. 3, what was the original expenditure of the mess ?

Accepted Answer

Let the average expenditure per head be Rs. p Now, the expenditure of the mess for old students is Rs. 44p After joining of 15 more students, the average expenditure per head is decreased by Rs. 3 => p-3 Here, given the expenditure of the mess for (44+15 = 59) students is increased by Rs. 33 Therefore, 59(p-3) = 44p + 33 59p - 177 = 44p + 33 15p = 210 => p = 14 Thus, the expenditure of the mess for old students is Rs. 44p = 44 x 14 = Rs. 616.

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