Question: 26 -

The average of non-zero number and its square is 5 times the number. The number is:

9

17

295

29

Answer:

9

Solution:

Let the number be x. Then, 
(x + x^2)/2 = 5x => x^2 - 9x = 0
=> x(x - 9) = 0
=> x = 0 or x = 9
So, the number is 9.

Question: 27 -

The average weight of A, B and C is 45 kg. If the average weight of A and B be 40 kg and that of B and C be 43 kg, then the weight of B is:

31 kg

17 kg

20 kg

26 kg

Answer:

31 kg

Solution:

Let A, B, C represent their respective weights. 
Then, we have:
A + B + C = (45 * 3) = 135 --- (i)
A + B = (40 * 2) = 80 --- (ii)
B + C = (43 * 2) = 86 --- (iii)
Adding (ii) and (iii), we get: A + 2B + C = 166 --- (iv)
Subtracting (i) from (iv), we get: B = 31
B's weight = 31 kg.

Question: 28 -

If the arithmetic mean of seventy five numbers is calculated, it is 35. If each number is increased by 5, then mean of new number is:

30

40

90

70

Answer:

40

Solution:

A.M. of 75 numbers = 35
Sum of 75 numbers = 75 * 35 = 2625
Total increase = 75 * 5 = 375
Increased sum = 2625 + 375 = 3000
Increased average = 3000/75 = 40.

Question: 29 -

The average monthly income of P and Q is Rs. 5050. The average monthly income of Q and R is 6250 and the average monthly income of P and R is Rs. 5200. The monthly income of P is:

4050

3500

4000

4055

Answer:

4000

Solution:

Let P, Q and R represent their respective monthly incomes. Then, we have:

P + Q = (5050 * 2) = 10100 --- (i)
Q + R = (6250 * 2) = 12500 --- (ii)
P + R = (5200 * 2) = 10400 --- (iii)
Adding (i), (ii) and (iii), we get: 
2(P + Q + R) = 33000 = P + Q + R = 16500 --- (iv)
Subtracting (ii) from (iv), we get, P = 4000.
P's monthly income = Rs. 4000.

Question: 30 -

Find the average of all numbers between 5 and 49 which are divisible by 5.

25

35

30

20

Answer:

25

Solution:

The numbers divisible by 5 are: 5, 10, 15, 20, 25, 30, 35, 40, 45.