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 :

Correct Answer: 37.5

Explanation:

Average speed = (2xy) /(x + y) km/hr

                      = (2 * 50 * 30) / (50 + 30) km/hr.

                         37.5 km/hr.

Correct Answer: 20

Explanation:

Let the initial number of persons be x. Then,

16x + 20 * 15 = 15.5 (x + 20) <=> 0.5x = 10 <=> x = 20.

Correct Answer: 29 yrs

Explanation:

Let the avg age of 7 boys be 'p' years
Let the age of the girl be 'q' years
From given data,
The age of 7 boys = 7p years
Now the new average = (p + 1) when 22 yrs is replaced by q
Now the age of all 7 will become = 7(p + 1) yrs
Hence, 7p - 22 + q = 7(p + 1) yrs
7p - 22 + q = 7p + 7
q = 22 + 7 = 29

Therefore, the age of girl = q = 29 years.

Correct Answer: 20 minutes

Explanation:

Let the total distance to be covered is 84 kms.
Time taken to cover the distance without stoppage = 84/42 hrs = 2 hrs
Time taken to cover the distance with stoppage = 84/28 = 3 hrs.
Thus, he takes 60 minutes to cover the same distance with stoppage.
Therefore, in 1 hour he stops for 20 minutes.

Correct Answer: 40.36

Explanation:

Given,

mean of 100 observations is 40

=> Total of 100 observations = 40 x 100 = 4000

84 is misread as 48

=> Difference = 84 - 48 = 36

=> Now, new total of 100 observations = 4000 + 36 = 4036

Correct Mean = 4036/100 = 40.36

Correct Answer: 84 km/hr

Explanation:

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.

Correct Answer: 120

Explanation:

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,

 

$$\begin{gathered} x + y + z 3 = 56 \\ 2 y + y + 4 y 3 = 56 ( From 1 & 2 ) \\ 7 y = 56 x 3 \\ y = 24 \end{gathered}$$

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.

Correct Answer: 3600

Explanation:

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

Correct Answer: 2

Correct Answer: 15 years

Explanation:

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