model 7 average on ages/weight Practice Questions Answers Test with Solutions & More Shortcuts

Question : 41

3 years ago, the average age of a family of 5 members was 17 years. A baby having been born, the average age of the family is same today. The present age of the baby is

a) 1 $1/2$ year

b) 1 year

c) 3 years

d) 2 years

Answer: (d)

Present age of child

= 17 × 6 – (17 × 5 + 3 × 5)

= 102 – (85 + 15) = 102 – 100

= 2 years

Question : 42 [SSC CHSL 2011]

Five years ago, the average age of P and Q was 25. The average age of P, Q and R today is 25. Age of R after 5 years will be

a) 20 years

b) 15 years

c) 35 years

d) 40 years

Answer: (a)

Sum of the present age of P and Q.

= 2 × 25 + 10 = 60 years

Sum of the present age of P, Q and R

= 25 × 3 = 75 years

∴ R’s present age = 75 – 60 = 15 years

∴ R’s age after 5 years = 20 years

Question : 43

In a class, there are 40 boys and their average age is 16 years. One boy, aged 17 years, leaving the class and another joining, the average age becomes 15.875 years. The age of the new boy is :

a) 14.5 years

b) 12 years

c) 17 years

d) 15 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

Question : 44

The average age of 30 students is 9 years. If the age of their teacher is included, the average age becomes 10 years. The age of the teacher (in years) is

a) 31

b) 27

c) 40

d) 35

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

Question : 45

The average age of 12 players of a team is 25 years. If the captain’s age is included, the average age increases by 1 year. The age of the captain is :

a) 38 yrs.

b) 25 yrs.

c) 26 yrs.

d) 36 yrs.

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

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