model 1 basic average questions Section-Wise Topic Notes With Detailed Explanation And Example Questions

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

Answer: (a)

Using Rule 2,

If the given observations (x) are occuring with certain frequency (A) then,

$Average = {A_1x_1+A_2x_2+...............+A_nx_n}/{x_1+x_2+......+x_n}$

Average income of whole group

= ${4200×40+4000×35}/75$

= ${168000+140000}/75$

= $308000/75$ =Rs. 4106$2/3$

Answer: (c)

Sum of first n odd natural numbers = $n^2$

∴ Their average = ${n^2}/n$ = n

∴ Required average = 25

because n = 25

Aliter : Using Rule 7,

Average = 25

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

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

Answer: (c)

Average cost of a chair

=Rs. x, then

x × 12 + 6 × 750 = 7800

⇒ 12x = 7800 – 4500 = 3300

⇒ x = $3300/12$ = Rs. 275