PROBLEMS ON AGES
Problem 1 :
The age of a man is three times the sum of the ages of his two sons and 5 years hence his age will be double the sum of their ages. Find the present age of the man.
Solution :
Let 'x' be the present age of the man and 'y' be the sum of the present ages of two sons.
Given : Present age of the man is 3 times the sum of the ages of 2 sons.
x = 3y ----(1)
Given : 5 years hence, age of the man will be double the sum of the ages of his two sons.
x + 5 = 2(y + 5 + 5)
(Here, 5 is added twice to y. Because, there are two sons in y)
x + 5 = 2(y + 10)
x + 5 = 2y + 20
From (1), we can plug x = 3y.
3y + 5 = 2y + 20
y = 15
Substitute y = 15 in (1).
x = 3(15)
x = 45
So, the present age of the man is 45 years.
Problem 2 :
Present age of a father is 3 years more than three times the age of his son. Three years hence, father's age will be 10 years more than twice the age of the son. Find the present age of the father.
Solution :
Let 'x' be the present age of the son and 'y' be the present age of the father.
Given : Present age of a father is 3 years more than three times the age of his son.
y = 3x + 3 ----(1)
Given : Three years hence, father's age will be 10 years more than twice the age of the son.
y + 3 = 2(x + 3) + 10
y + 3 = 2x + 6 + 10
y + 3 = 2x + 16
From (1), substitute y = 3x + 3.
3x + 3 + 3 = 2x + 16
3x + 6 = 2x + 16
x = 10
Substitute x = 10 in (1).
y = 3 ⋅ 10 + 3
y = 33
So, the present age of the man is 33 years.
Problem 3 :
The ratio of the age of a man and his wife is 4 : 3. After 4 years this ratio will become 9 : 7. At the time of marriage, if the ratio was 5 : 3, how many years ago were they married ?
Solution :
Given : The ratio of the present ages of a man and his wife is 4 : 3.
Then, the present age of the man is 4x and his wife is 3x.
Given : After 4 years this ratio will become 9 : 7.
(4x + 4) : (3x + 4) = 9 : 7
(4x + 4)/(3x + 4) = 9/7
7(4x + 4) = 9(3x + 4)
28x + 28 = 27x + 36
x = 8
So, the present age of the man is
= 4x
= 4 ⋅ 8
= 32 years
The present age of his wife is
= 3x
= 3 ⋅ 8
= 24 years
Let us assume that they got married before 't' years from now.
Given : At the time of marriage, if the ratio was 5 : 3.
(32 - t) : (24 - t) = 5 : 3
(32 - t)/(24 - t) = 5/3
3(32 - t) = 5(24 - t)
96 - 3t = 120 - 5t
2t = 24
t = 12
So, they got married 12 years before.
Problem 4 :
John's age after six years will be three seventh of his father's age. Ten years ago the ratio of their ages was 1 : 5 . What is John's father's age at present ?
Solution :
Given : Ten years ago the ratio of their ages was 1 : 5.
Then, ten years ago,
age of John = x
age of his father = 5x
At present,
age of John = x + 10
age of his father = 5x + 10
After six years,
age of John = x + 10 + 6 = x + 16
age of his father = 5x + 10 + 6 = 5x + 16
Given : John's age after six years will be three seventh of his father's age.
(x + 16) = (3 / 7)(5x + 16)
7(x + 16) = 3(5x + 16)
7x + 112 = 15x + 48
64 = 8x
8 = x
At present, John's father's age is
= 5x + 10
Substitute x = 8.
= 5 ⋅ 8 + 10
= 40 + 10
= 50
So, the present age of John's father is 50 years.
Problem 5 :
The total age of P and Q is 12 years more than the total age of Q and R. R is how many year younger to P ?
Solution :
From the given information, we have
P + Q = 12 + Q + R
When we rearrange the above equation, we get
P - R = 12 + Q - Q
P - R = 12
From the above equation, it is clear that R is 12 years younger to P.
Kindly mail your feedback to v4formath@gmail.com
We always appreciate your feedback.
WORD PROBLEMS
Word problems on simple equations
Word problems on linear equations
Word problems on quadratic equations
Area and perimeter word problems
Word problems on direct variation and inverse variation
Word problems on comparing rates
Converting customary units word problems
Converting metric units word problems
Word problems on simple interest
Word problems on compound interest
Word problems on types of angles
Complementary and supplementary angles word problems
Markup and markdown word problems
Word problems on mixed fractions
One step equation word problems
Linear inequalities word problems
Ratio and proportion word problems
Word problems on sets and Venn diagrams
Pythagorean theorem word problems
Percent of a number word problems
Word problems on constant speed
Word problems on average speed
Word problems on sum of the angles of a triangle is 180 degree
OTHER TOPICS
Time, speed and distance shortcuts
Ratio and proportion shortcuts
Domain and range of rational functions
Domain and range of rational functions with holes
Graphing rational functions with holes
Converting repeating decimals in to fractions
Decimal representation of rational numbers
Finding square root using long division
L.C.M method to solve time and work problems
Translating the word problems in to algebraic expressions
Remainder when 2 power 256 is divided by 17
Remainder when 17 power 23 is divided by 16
Sum of all three digit numbers divisible by 6
Sum of all three digit numbers divisible by 7
Sum of all three digit numbers divisible by 8
Sum of all three digit numbers formed using 1, 3, 4
Sum of all three four digit numbers formed with non zero digits
Sum of all three four digit numbers formed using 0, 1, 2, 3
Sum of all three four digit numbers formed using 1, 2, 5, 6
©All rights reserved. onlinemath4all.com
Recent Articles
-
Linear Growth and Decay
May 22, 22 03:05 AM
Linear Growth and Decay
-
Worksheet on Probability
May 22, 22 01:15 AM
Worksheet on Probability
-
Probability Worksheet
May 22, 22 01:12 AM
Probability Worksheet