Quantitative Aptitude: Averages Quiz 2

Q1.The average age of a group of friends is 34 years. If five new friends with an average age of 30 years join the group, the average age of the entire group becomes 32 years. How many people were there in the group initially?

Solution

Old
combined age = 34x

New
combined age

= (5 + x)
x 32 = 34x + (5 x 30)

Þ 32x + 160 = 34x + 150

\ x = 5

Q2. If 20 kg of wheat costing Rs 16 a kg is mixed with Rs, 16 kg of a second variety of wheat costing Rs 25 a kg, then what is the average cost of the resulting mixture?

Solution

Avg = (20
x 16 + 16 x 25)/ (20 + 16)

= 720/36
= 20

Q3. If two kinds of grapes costing Rs 16 a kg and Rs 21 a kg are mixed in the ratio of 2 : 3 then find the cost of mixture per kg?

Solution
Avg = (16 x 2 + 21 x 3)/
(2+3) = 95/9 = 19

Q4. If 15 litres of 20% alcohol is mixed with 2 litres of 24% alcohol, then find the concentration of the resulting solution?

588/97
588/27
588/57
588/7

Solution
(15 x 20+ 12 x 24)/(15 + 12) = (588)/ 27

Q5.Find two numbers whose AM is 12.5 and GM is 10?

20,15
18,24
20,5
12,16

Solution
a + b =
25; ab = 100

a + 100/a
= 25

Þ a² + 100 – 25a = 0 Þ a² – 25a + 100 = 0

Þ a² – 20a – 5a + 100 =
0

Þ a(a-20) – 5(a-20) = 0

Þ (a-5)(a-20) = 0

Therefore,
a = 5 or a = 20

If a = 5;
b = 20

If b =
20; a = 5

Q6. The average age of a husband and his wife was 23 years at the time of their marriage. After five years they have one-year old child. The average age of the family now is:

19 years
73 years
28.5 years
29.3 years

Solution
New avg. age=((23+23)+(5+5)+1}/3 =19

Q7. The average salary of all the workers in a workshop is Rs. 8000. The average salary of 7 technicians is Rs.12000 and the average salary of the rest is Rs. 6000. The total number of workers in the workshop is:

Solution

8000 =