1. The average age of Ram, Venu, Kumar, Gopal and Ragav
is 28 years. The average age of Gopal and Ragav is 25 years. What is the
average age of Ram, Venu and Kumar ?
Solution :
Here 5 persons' average ( Ram, Venu, Kumar, Gopal
and Ragav) age is = 28 Years.
That means their total age = 5 X 28 = 140 Years.
similarly, average age of two persons (Gopal and Ragav)
is 25 years.
So their total age = 25 X 2 = 50 Years.
here 140 years is the total age of 5
persons
( Ram, Venu, Kumar, Gopal and Ragav)
50 years is the total age of 2 persons (Gopal and Ragav)
So obviously, the total age of Ram, Venu and Kumar
= Total age of ( Ram, Venu, Kumar, Gopal and Ragav)
- Total age of (Gopal and Ragav)
= 140-50 = 90 years.
But here we need average age of these 3 persons.
=> 90/3 = 30 Years
Shortcut Method :
((5 X 28) - (2 X 25)) / 3 = (140-50)/ 3 =
90/3 = 30 Years
2. The ratio between the ages of Keerthi and Sony
is 5:8 respectively and difference between their ages after 5 years will be 12
years. What is the present age of Keerthi ?
Solution :
Usually for these type of questions people start
with present age as X and adding 5 to get the ages after 5 years and
later solve those equations. But its very time consuming.
A simple logic here is if the age difference
between you and your friend is 8 years, after 5 or 10 years also the difference
will be same. Hope you are getting what I am trying to say ;)
now see, the ratio between their ages is 5 :
8
That means their actual ages will be some 5X and
8X
Then the difference between their ages is
5X-8X
in the question it is given that the difference is
12 years => 5X-8X = 12 => 3X=12 => X = 4
So obviously Keerthi's age = 5(4) = 20
3. Sony is 30 years younger than his mother Rani.
Five years ago, Sony was 1/4 as old as his mother was. How old is Sony today ?
Solution :
5 years ago the ratio between their ages was Sony : Jay a= 1X
: 4X
we know that Hari is 30 years younger than Rani.
That means the difference between their ages is 30.
=> 3X = 30 => X = 10.
But this is the age of 5 years ago. So, the present
age will be =10+5 = 15 Years
4. At present the ratio of the ages of Anand and Venkat
is 4 : 7 respectively. 6 years hence it will be 7 : 10 respectively. What is
the present age of Venkat ?
Solution :
Present ratio of their ages is 4 : 7 (So their
present ages will be 4X, 7X)
After six years it will be of 7 : 10
=> (4x+6) : (7x+6) = 7 : 10
=> 40x + 60 = 49X + 42 (Cross Multiplication)
=> 9x = 18
=> x =
2
So Venkat's present age will be 7X2 = 14 Years
Shortcut :
There is a shortcut formula for finding X
here, New ratio difference is 3, Added number is 6
(years)
Cross multiplication difference is 49-40 = 9
=> X = (3 x
6) / 9 = 2
So Venkat's present age will be 7X2 = 14 Years
5. Ten years ago the ratio between the ages of
Mohan and Suman was 3:5 respectively. 11 years hence it will be 11:16
respectively. What is the present age of Mohan?
Solution :
10 years ago 3x : 5x ------------->
Old Ratio
11 years hence 11x :
16x -------------> New Ratio
here the difference between ages is 21 years (10
years ago + 11 years hence)
apply above formula here
New ratio difference is (16-11) = 5
Added or substracted number (difference between
ages) is = 21
Old and new ratios cross multiplication difference
is = 55 - 48 = 7
==> X = (5 x 21) / 7 = 15
present age of mohan is = his age of 10 years ago +
10
= 3x15 + 10 = 55 years
6. Amar is as much younger than Raja as he is older
than Kiran. If the ages of Amar and Raja are 30 years and 36 years
respectively, what is the age of Kiran now ?
Solution :
Simple logic....
Amar is as much younger than Raja as he is older
than Kiran. Try to understand this sentence. According to this sentence you can
understand that
·
Amar is
younger than Raja that means there is some X years difference between Amar and
Raja.
·
Amar is
older than Kiranwith same age difference (X years) between Amar and Kiran.
But we know that the ages of Amar and Raja are 30
and 36 years.
So the difference between their ages is = 6 years
So the difference between Amar and Kiran should be
= 6 years.
We know the age of Amar as 30 years and Kiran is
younger than Amar for 6 years. So he should be of 24 years.
With a single glance you can calculate answer for
these type of problems.
7. The average age of a class of 20 students is 20
years. When the age of the teacher is also included, the average will be increased
by 2 years. What is the age of the teacher ?
Solution :
Simple logic,
we know that 20 students' average = 20 years
20 people total age = 20 x 20 = 400 years
Including Teacher's
21 people average = 22 years
21 people total age = 21 x 22 = 462
we know the age of 20 students = 400 Yeras
we know the age of 21 people (20 students+ Teacher)
= 462
so the age of Teacher will be 462-400 = 62 Years
8. The average age of a wife and husband, who were
married 10 years ago, was 20 years then. Including a child the present average
age of the family is 23 years. What is the present age of the child?
Solution :
10 year's ago average age = 20 years
10 year's ago total age = 20 x 2 = 40 years.
to calculate their present total age, you should
add 20 (10 for wife and 10 for husband) to the age of 10 years ago
=> 40+20 = 60 years (this is the present age of
husband and wife) ----------- (1)
according to the given data, present average age of
the family of 3 members is = 23 years
so Total age of 3 members = 23 x 3 = 69 years. ------------------(2)
but we know the present age of Husband and Wife =
60 years
so from equations (1) and (2), we can get the
present age of the child is = 9 years
9. Five years ago the average age of a family of
five members was 27 years then. Including a child the present average age is
still same today. What is the age of the child now ?
Solution :
5 years back average = 27 years
present average should be 5 +27 = 32 Years
So total age of the 5 members at present = 5 x 32 =
160 years -----------------(1)
but its given that including the child, the present
average is 27 years.
=> the total age of 6 members at
present = 6 x 27 = 162 years -----------------(2)
so from (1) and (2), you can easily get that the
present age of the child is 2 years
10. The ratio between the ages of Karan and Arjun
is 9:5 and sum of their ages at present is 56 years. How old will karan be
after 4 years ?
Solution :
according to given data their ages should be 9x, 5x
their present age = 9x+5x = 56 ==> 14x =
56
so x = 4
so present age of Karan is 9 x 4 = 36 years
after 4 years, 36+4 = 40 years :)
