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

Answer: (a)

Sum of total number of 8 students in exam = 8 × 51 = 408

Sum of total number of 9 students in exam = 9 × 68 = 612

∴ Required average

= ${408+ 612}/17$ =${1020}/17$ = 60

Aliter : Using Rule 10,

Here, $n_1$ = 8, $a_1$ = 51

$n_2$ = 9, $a_2$ = 68

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

${8×51+9×68}/{8+9}$

${408+612}/17$ = $1020/17$

= 60 marks.

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: (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

Answer: (c)

Let the average cost of each book bought (of 64 books) be Rs.x.

According to the question,

64 × x – 50(x + 1) = 76

⇒ 64x – 50x – 50 = 76

⇒ 14x = 76 + 50 = 126

⇒ x = $126/14$ = 9

∴ Required average price

= 9 + 1 = Rs. 10