model 7 average on ages/weight Section-Wise Topic Notes With Detailed Explanation And Example Questions

Answer: (a)

Easy method:

Average age of new players

= { (20+17)11×$2/12$ }×$1/2$

$422/{12×2}$ =$211/12$⇒ 17$7/12$

= 17 years 7 months

Answer: (b)

Average age of 4 brothers = 12 yrs.

Total age of 4 brothers = 4 × 12 = 48 yrs.

Average age of 4 brothers + mother ( = 5 persons) = 12 + 5 = 17 yrs.

∴Total age of 4 brothers + mother = 5 × 17 = 85 yrs.

∴The age of the mother = 85 – 48 = 37 yrs.

Aliter : Using Rule 24,

( If a new member is added in a group then. age (or income) of added member = Average (or income) ± x (n + 1)

where x = increase (+) or decrease (–) in average age (or income) n = Number of members. )

Here, x = 5, n = 4

Age of mother = Average+x (n+1)

= 12 + 5 (4 + 1)

= 12 + 25 = 37 years

Answer: (a)

Total age decreased = 10 × 3 = 30 years.

∴ Age of the retired teacher = 25 + 30 = 55 years.

Aliter : Using Rule 23,

Here, n = 10, x = 3

Age of new teacher = Age of retired teacher – xn

25 = Age of retired teacher – 10 × 3

= Age of retired teacher

= 25 + 30 = 55 years

Answer: (a)

Total age of 12 players = 12 × 25 = 300

Total age including captain = 13 × 26 = 338

∴ Age of the captain = 338 – 300 = 38 years

Aliter : Using Rule 23,

( If in a group, one member is replaced by a new member, then,

Age of new member = ( age of replaced member) ± xn

where, x = increase (+) or decrease (–) in average n = Number of members. )

Here, x = 1, n = 12

Age of the captain = Average + x (n + 1)

= 25 + 1 (12 + 1) = 38 years

Answer: (c)

Total age of 30 students = 9 × 30 = 270 years

Total age of 30 students and a teacher = 31×10 = 310 years

∴ Age of the teacher = 310 – 270 = 40 years

Answer: (b)

Total age of 40 boys = 40 × 16 = 640 years

New total age of 40 boys = 40 × 15.875 = 635 years

∴ Age of new boy = [635 – (640–17)] = 12 years

Aliter : Using Rule 23,

Here, n = 40, x = 16 – 15.875, x = 0.125

Age of new boy = Age of replaced boy–xn

= 17 – 0.125 × 40

= 17 – 5 = 12 years