model 1 basic average questions Practice Questions Answers Test with Solutions & More Shortcuts

Question : 16 [SSC Multi-Tasking Staff 2013]

Six tables and twelve chairs were bought for Rs.7,800. If the average price of a table is Rs.750, then the average price of a chair would be

a) Rs.150

b) Rs.175

c) Rs.275

d) Rs.250

Answer: (c)

Average cost of a chair

=Rs. x, then

x × 12 + 6 × 750 = 7800

⇒ 12x = 7800 – 4500 = 3300

⇒ x = $3300/12$ = Rs. 275

Question : 17 [SSC CGLTier-I 2012]

The average monthly expenditure of a family is Rs.2,200 during first three months,Rs.2,550 during next four months and Rs.3,120 during last five months of the year. If the total savings during the year was Rs.1,260, what is the average monthly income ?

a) Rs.2,805

b) Rs.2,850

c) Rs.1,280

d) Rs.1,260

Answer: (a)

Using Rule 1,

Average of two or more numbers/quantities is called the mean of these numbers, which is given by

$\text"Average(A)" = \text"Sumof observation / quantities"/\text"No of observation / quantities"$

∴ S = A × n

Total expenditure of the year

= Rs.(3 × 2200 + 4 × 2550 + 5 × 3120)

= Rs. (6600 + 10200 + 15600)

= Rs.32400

∴ Total income of the year

= Rs. (32400 + 1260)

= Rs.33660

∴ Average monthly income

= Rs.$33660/12$ = Rs. 2805

Question : 18 [SSC FCI 2013]

There are two groups A and B of a class, consisting of 42 and 28 students respectively. If the average weight of group A is 25 kg and that of group B is 40 kg, find the average weight of the whole class.

a) 70 kg

b) 30 kg

c) 31 kg

d) 69 kg

Answer: (c)

Required average weight

= ${42×25+28×40}/{42+28}$

= ${1050+1120}/70$ = $2170/70$ = 31kg

Aliter : Using Rule 10,

Here, $n_1$ = 42, $a_1$ = 25

$n_2$ = 28, $a_2$ = 40

∴ Average = ${n_1a_1+ n_2a_2}/{n_1+ n_2}$

Question : 19 [SSC CISF 2010]

The mean of 9 observations is 16. One more observation is included and the new mean becomes 17. The 10th observation is

a) 26

b) 30

c) 16

d) 9

Answer: (a)

Mean of Ten observations – Mean of nine observations

Tenth observation

= 10 × 17 – 16 × 9

= 170 – 144 = 26

Aliter : Using Rule 19,

Here, N = 9, T = 16

n = 1, t = 1

10th observation

= T+ $({N/n}+1)$t

= 16+$(9/1+1) ×1$

= 16 + 10 = 26

Question : 20 [SSC CAPFs SI, CISF 2015]

The average of some natural numbers is 15. If 30 is added to first number and 5 is subtracted from the last number the average becomes 17.5 then the number of natural number is

a) 20

b) 10

c) 30

d) 15

Answer: (b)

Number of natural numbers = x

∴ Their sum = 15x

According to the question,

15x + 30 – 5 = x × 17.5

⇒ 17.5x – 15x = 25

⇒ 2.5x = 25

⇒ x = $25/2.5$ = 10

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