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

Question : 6 [SSC CGL Tier-I 2010]

In a family, the average age of a father and a mother is 35 years. The average age of the father, mother and their only son is 27 years. What is the age of the son ?

a) 11 years

b) 12 years

c) 10 years

d) 10.5 years

Answer: (a)

Father + mother = 2 × 35 = 70 years

Father + mother + son = 27 × 3 = 81 years

∴ Son’s age = 81 – 70 = 11 years

Question : 7

The average age of 8 men is increased by 2 years when two of them whose age are 21 and 23 years replaced by two new men. The average age of the two new men is

a) 24 years

b) 22 years

c) 30 years

d) 28 years

Answer: (c)

Overall increase in the total age = 8 × 2 = 16 years

∴ Total age of two new men = 21 + 23 + 16 = 60 years

∴ Average age of new men = $60/2$ = 30 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 = 2, n = 8

Age of new person = Age of replaced person + x

= 24 + 2 × 8

= 24 + 16 = 40 years

Question : 8 [SSC CGL Tier-I 2013]

In a family of 5 members, the average age at present is 33 years. The youngest member is 9 years old. The average age of the family just before the birth of the youngest member was

a) 29 years

b) 30 years

c) 24 years

d) 25 years

Answer: (b)

Sum of the present age of family members = 33 × 5 = 165 years 9 years ago,

Sum of their age = 165 – 9 × 5 = 120 years

∴ Required average age = $120/4$ = 30 years

Question : 9 [SSC Investigator 2010]

The average age of 9 students and their teacher is 16 years. The average age of the first four students is 19 years and that of the last five is 10 years. The teacher’s age is

a) 34 years

b) 36 years

c) 28 years

d) 30 years

Answer: (a)

Teacher’s age

= 16 × 10 – 19 × 4 – 5 × 10

= 160 – 76 – 50 = 34 years

Question : 10 [SSC CGL Tier-II 2012]

In a school with 600 students, the average age of the boys is 12 years and that of the girls is 11 years. If the average age of the school is 11 years and 9 months, then the number of girls in the school is

a) 150

b) 450

c) 350

d) 250

Answer: (a)

Number of girls = x

Number of boys = 600 – x

∴ (600 – x ) × 12 + 11x

= 11$3/4$×600 = $47/4$ × 600

⇒ 7200 – 12x + 11x = 7050

⇒ x = 7200 – 7050 = 150

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