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

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

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: (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: (d)

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

Average height

= ${6×1.15+8×1.1+6×1.12}/20$

= ${6.9+8.8+6.72}/20$ = ${22.42}/20$

= 1 metre 12.1 cm

Answer: (d)

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

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

Students in class A ⇒ x

Students in class B ⇒ y

Students in class C ⇒ z

For classes A and B,

${83x + 76y}/{x+y}$ = 79

⇒ 83x + 76y = 79x + 79y

⇒ 83x – 79x = 79y – 76y

⇒ 4x = 3y

For classes B and C

${76y+85z}/{y+z}$= 81

⇒ 76y + 85z = 81y + 81z

⇒ 5y = 4z

∴ 20x = 15y = 12z

⇒ ${20x}/60$ = ${15y}/60$ = ${12z}/60$

⇒ $x/3$ = $y/4$ = $z/5$

∴ Required average

${83×3+76×4+85×5}/{3+4+5}$

${249+304+425}/12$ = $978/12$

= 81.5

Answer: (c)

Difference = 83 – 53 = 30

Incorrect observation > Correct observation

∴ Required average

= 35 - $30/100$ = 35 – 0.3 = 34.7