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

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: (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: (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

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