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

Question : 11 [SSCCHSL 2011]

The average age of 45 persons is decreased by $1/9$ year when one of them of 60 years is replaced by a new comer. Then the age of the new comer is :

a) 55 years

b) 45 years

c) 49 years

d) 59 years

Answer: (a)

Reduction in total age of 45 persons = 45 × $1/9$

Age of the new person

= 60 – 45 × $1/9$ = 55 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. )

Age of new corner = Age of replaced member – xn

= 60 – 45 × $1/9$

= 60 – 5 = 55 years

Question : 12 [SSC CGL Prelim 2007]

From a class of 24 boys, a boy, aged 10 years, leaves the class and in his place a new boy is admitted. As a result, the average age of the class is increased by 2 months. What is the age of the new boy ?

a) 15 years

b) 12 years

c) 13 years

d) 14 years

Answer: (d)

Total age increase = 2 × 24 = 48 months = 4 years

∴ Age of the new boy = 10 + 4 = 14 years.

Question : 13

The average age of 40 students of a class is 18 years. When 20 new students are admitted to the same class, the average age of the students of the class is increased by 6 months. The average age of newly admitted student is

a) 19 years 6 months

b) 19 years

c) 20 years 6 months

d) 20 years

Answer: (a)

Total age of 20 new students

= (60 × 18.5 – 40 × 18) years

= (1110 – 720) years

= 390 years

∴ Their average age = $390/20$ = 19.5 years

= 19 years 6 months

Question : 14 [SSC CHSL 2015]

In a class there are 30 boys and their average age is 17 years. On one boy aged 18 years leaving the class and another joining, the average age becomes 16.9 years. The age of new boy is

a) 11 years

b) 25 years

c) 15 years

d) 13 years

Answer: (c)

Age of new boy = 18 years – total decrease

= (18 – 0.1 × 30) years = 15 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 = 17 – 16.9 = 0.1, n = 30

Age of new boy

= Age of replaced boy–xn

= 18 – 0.1 × 30

= 18 – 3 = 15 years

Question : 15 [SSC CPO 2003]

The average age of 20 boys in a class is 12 years. 5 new boys are admitted to the class whose average age is 7 years. The average age of the boys in the class becomes

a) 9.5 years

b) 8.2 years

c) 11 years

d) 12.5 years

Answer: (c)

New average age of class

= ${20 × 12 + 5 × 7}/25$ = ${240+35}/25$

= $275/25$ = 11 years

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