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

Answer: (a)

Number of students in section A = x

∴ Number of students in sections B and C

= (100 – x)

∴ x × 70 + (100 – x) × 87.5

= 84 × 100

⇒ 70x + 87.5 × 100 – 87.5x = 8400

⇒ 8750 – 17.5x = 8400

⇒ 17.5x = 8750 – 8400 = 350

⇒ x = $350/{17.5}$ = 20

Answer: (c)

Sum of x numbers = xy

Sum of y numbers = xy

∴ Required average = ${xy+xy}/{x+y}$ = ${2xy}/{x+y}$

Aliter : Using Rule 10,

Here, $n_1$ = x, $a_1$ = y

$n_2$ = y, $a_2$ = x

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

= ${xy+yx}/{x+y}$ = ${2xy}/{x+y}$

Answer: (c)

Using Rule 2,

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

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

where, $A_1, A_2, A_3, .......... A_n$ are frequencies

Required average price

= ${13×70+15×60+12×65}/{13+15+12}$

= ${910+900+780}/40$ =$2590/40$

= Rs.64.75

Answer: (c)

Total sum of x numbers = x$y^2$

Total sum of y numbers = y$x^2$

∴ Required average

= ${xy^2+yx^2}/{x+y}$

=${xy(y+x)}/{x+y}$ = xy

Aliter : Using Rule 10,

Here, $n_1$ = x, $a_1$ = $y^2$

$n_2$ = y, $a_2$ = $x^2$

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

= ${xy^2+yx^2}/{x+y}$

= xy$({x+y}/{x+y})$ = xy

Answer: (a)

Weight of 12th person = x kg (let).

∴ Average weight of 12 persons

= $({11×95+x}/12)$kg

According to the question,

${11×95+x}/12$ +33 = x

⇒ 1045 + x + 396 = 12x

⇒ 1441 = 11x

⇒ x = $1441/11$ = 131 kg.

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

Number of workers in the factory = $1534/118$ = 13