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

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

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: (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: (c)

Let average marks of remaining 30 students be x.

∴ 65 = ${30×85+30×x}/60$

⇒ 65 × 60 = 2550 + 30x

⇒ 3900 = 2550 + 30x

⇒ 30x = 3900 – 2550 = 1350

⇒ x = $1350/30$ = 45.

Answer: (a)

Male employees = x

Female employees = y

∴ (x + y) 12000 = x × 15000 + y × 8000

⇒ (x + y) × 12 = 15x + 8y

⇒ 12x + 12y = 15x + 8y

⇒ 3x = 4y

⇒ $x/y$ = $4/3$ ⇒ x : y = 4 : 3

Answer: (b)

Using Rule 10,

If the average of '$n_1$' numbers is $a_1$ and the average of '$n_2$' numbers is $a_2$, then average of total numbers $n_1$ and $n_2$ is

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

Required average weight

$(50×6+51×2+55×2)/10$

= ${300+102+110}/10$ = $512/10$

= 51.2 kg