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

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: (d)

B’s weight = (A + B)’s weight + (B + C)’s weight – (A + B + C)’s weight

= (40 × 2 + 2 × 43 – 45 × 3) kg.

= (80 + 86 – 135) kg.

= 31 kg.

Answer: (c)

Weight of the boat

= 6 × 52 – 5 × 38

= 312 – 190 = 122 kg

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: (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)

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