# Averages Quiz Set 005

### Question 1

The average weight of 18 students of a class is 29 Kg, whereas the average weight of remaining 12 students is 32 Kg. What is the average weight of all 30 students?

A

\$30{1/5}\$.

B

\$31{7/29}\$.

C

\$29{7/31}\$.

D

\$32{5/14}\$.

Soln.
Ans: a

Total weight of 18 students is 18 × 29 = 522. Similarly, the total weight of remaining 12 students is 12 × 32 = 384. The total weight of all 30 students is 522 + 384 = 906. So the average = 906/30 = \$30{1/5}\$.

### Question 2

Average weight of a group of 41 boys is 75 Kg. Later it was found that the weighing machine was showing 4 Kg more than the actual weight. What is the actual average weight?

A

71.

B

72.

C

70.

D

69.

Soln.
Ans: a

Let the total weight of the group as measured with the faulty machine be x. Then, by average formula \$75 = x/41\$, which gives x = \$75 × 41 = 3075\$. When weight of each of the 41 boys is reduced by 4 Kg, the new total becomes \$3075 - 41 × 4 = 2911\$, the new average becomes \$2911/41 = 71\$. TIP: As a shortcut, the new average = old average - error in weighing machine.

### Question 3

A, B and C are three numbers. The average of A, B and C is 31. The average of A and B is 17, and the average of B and C is 43, what is the value of number B?

A

27.

B

28.

C

26.

D

25.

Soln.
Ans: a

By the given conditions, A + B = 2 × 17 = 34. Similarly, B + C = 2 × 43 = 86. Adding we get A + 2B + C = 120. We have also been given that A + B + C = 3 × 31 = 93. Subtracting, we get B = 120 - 93 = 27.

### Question 4

If the average of p and q is 20, the average of q and r is 48, and of r and p is 60, then what is the value of p?

A

32.

B

33.

C

31.

D

34.

Soln.
Ans: a

We have three equations (p + q)/2 = average of pq, (q + r)/2 = average of qr and (r + p)/2 = average of rp. Adding these three we get p + q + r = (average of pq + average of qr + average of rp) = (20 + 48 + 60) = 128. So p = 128 - (q + r) = 128 - (2 × average of q and r) = 128 - 2 × 48 = 32.

### Question 5

The sales(in rupees) of a gift shop for six consecutive days is 2160, 2100, 3234, 3636, 1932 and 4266. What is the overall average sale for these six days?

A

Rs.2888.

B

Rs.2894.

C

Rs.2882.

D

Rs.2900.

Soln.
Ans: a

The total sale on first six days is 2160 + 2100 + 3234 + 3636 + 1932 + 4266 = 17328. The average for 6 days is: 17328/6, which gives Rs. 2888. 