Problems on Ages

How To Solve Ages Questions Quickly

Important things to remember on How To Solve Ages Questions Quickly are given below:

Decide which age – either it is present or past or future.
After deciding the age, Consider it as X.
In most cases, we take the present age as ‘X’, i.e., the base year works just fine.
Past will express as (x-5) years.
The future can be expressed as (x+5).
But sometimes, ‘present age’ is not directly given in words. Then, take ‘x’ to be the age you are going to find.
Sometimes when nothing works then just look at the options and solve it through back calculations! It also works fine.

Some Exmple Questions to Understand How to solve

1. A boy asks his father, ” what is the age of grandfather?”. Father replied ” He is x years old in $x^{2}$ years”, and also said, “we are talking about the 20th century”. what is the year of birth of grandfather?

Options:

A) 1995

B) 1892

C) 1895

D) 1893

Solution:

20th century means 1900 to 2000

as He is x years old in $x^{2}$ years

only square year in the 20th century is $44^{2}$ = 1936

so Grandfather is 44 years old in 1936

& year of birth of grandfather is = 1936 - 44 = 1892.

Correct option: C

2. Seven years ago, the combined ages of A and B was twice that of C. If the sum of the ages of B and A, fifteen years hence, is 98 years, what is the present age of C?

Options:

A. 27 yrs

B. 35 yrs

C. 34 yrs

D. 49 yr

Solution:

A - a

B - b

C - c

(a - 7) + (b - 7) = 2(c - 7)

a + b – 14 = 2c – 14

a + b = 2c

a + b + 30 = 98

c = $\frac{68}{2}$ =34 yrs.

Correct option: C

3. The father's age is six times his son's age. Four years hence, the age of the father will be four times his son's age. The present ages, in years, of the son and the father are respectively,

Options:

A. 3 and 30 yrs

B. 6 and 36 yrs

C. 5 and 32 yrs

D. 3 and 35 yrs

Solution:

Let the present age of father's be x years and present age of son's be y years.

According to the problem

x=6y

After 4 years

x+4=4(y+4)

Hence we get two equations

x=6y ......... (1)

x+4=4(y+4) ..... (2)

Simplifying eq (2)

x+4=4y+16

x−4y=12

Put x=6y in eq (2), we get

6y−4y=12

2y=12

y=6 years and x=6y=36 years

Present age of son = 6 years and present age of father = 36 years

Correct Option: B

3.In a shopping mall with a staff of 5 members, the average age is 45 years. After 5 years a person joined them and the average age is again 45 years. What is the age of 6th person?

Options:

A. 35

B. 23

C. 20

D. 21

Solution:

lThe Average age of 5 person after 5 yrs will be 50 yrs.

so total age of 5 person $ = 50 \times 5 = 250$

and total age of 6 person $ = 45 \times 6 = 270$

so age of 6th person $ = 270 - 250 = 20$ yrs

Correct Option: C

3. Persons standing in the queue with different age group, after two years their average age will be 43 and the seventh person joined with them. hence the current average age has become 45. find the age of the seventh person?

Options:

A. 69

B. 70

C. 40

D. 45

Solution:

Let the age of 6 persons is x

after two years age will be = (x + 12)

average age = 43

therefore$ \frac{x+12}{6}$

$\implies x = 246 $

$ \frac{\text{x + 7th person age}}{7} = \frac{\text{246 + 7th person age}}{7} = 45 $(average age)

(by solving) the 7th person age is 69

Correct Option: A

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