**Problem 1 :**

Martin is four times as old as his brother Luther at present. After 10 years he will be twice the age of his brother. Find their present ages.

**Solution : **

Let 'x' and 'y' be the present ages of Martin and Luther respectively.

**Given :** Martin is four times as old as his brother Luther at present.

Then,

x = 4y ----(1)

**Given :** After 10 years, Martin will be twice the age of his brother Luther.

Then,

x + 10 = 2(y + 10)

x + 10 = 2y + 20

Subtract 10 from each side.

x = 2y + 10 ----(2)

From (1) and (2),

4y = 2y + 10

Subtract 2y from each side.

2y = 10

Divide each side by 2.

y = 5

Substitute 5 for y in (1).

(1)----> x = 4(5)

x = 20

So, the present ages of martin and Luther are 20 years and 5 years respectively.

**Problem 2 :**

A father is 30 years older than his son,and one year ago he was four times as old as his son. Find the present ages of his father and his son.

**Solution : **

Let 'x' and 'y' be the present ages of father and son respectively.

**Given :** A father is 30 years older than his son

Then,

x = y + 30 ----(1)

**Given :** One year ago, father was four times as old as his son.

Then,

x - 1 = 4(y - 1)

x - 1 = 4y - 4

Add 1 to each side.

x = 4y - 3 ----(2)

From (1) and (2),

y + 30 = 4y - 3

Subtract y from each side.

30 = 3y - 3

Add 3 to each side.

33 = 3y

Divide each side by 3.

11 = y

Substitute 5 for y in (1).

(1)----> x = 11 + 30

x = 41

So, the present ages of father and son are 41 years and 11 years respectively.

**Problem 3 :**

The ages of Abraham and Adam are in the ratio 5 : 7. Four years from now, the ratio of their ages will be 3 : 4. Find the present ages of them.

**Solution : **

**Given :** The ages of Abraham and Adam are in the ratio

5 : 7

Then,

age of Abraham = 5x

age of Adam = 7x

Four years from now,

age of Abraham = 5x + 4

age of Adam = 7x + 4

**Given :** Four years from now, the ratio of their ages will be

3 : 4

Then,

(5x + 4) : (7x + 4) = 3 : 4

(5x+4) / (7x+4) = 3 / 4

4(5x + 4) = 3(7x + 4)

20x + 16 = 21x + 12

Subtract 20x from each side.

16 = x + 12

Subtract 12 from each side.

4 = x

Then

5x = 5(4) = 20

7x = 7(4) = 28

So, the present ages of Abraham and Adam are 20 years and 28 years.

**Problem 4 :**

Airi's mother is four times as old as Airi. After five years her mother will be three times as old as she will be then. Find their present ages.

**Solution : **

Let 'x' and 'y' be the present ages of Mother and Airi respectively.

**Given :** Airi's mother is four times a old as Airi.

Then,

x = 4y ----(1)

**Given :** After five years Airi's mother will be three times as old as Airi will be then.

Then,

x + 5 = 3(y + 5)

x + 5 = 3y + 15

Subtract 5 from each side.

x = 3y + 10 ----(2)

From (1) and (2),

4y = 3y + 10

Subtract 3y from each side.

y = 10

Substitute 10 for y in (1).

(1)----> x = 4(10)

x = 40

So, the present ages of Airi's mother and Airi are 40 years and 10 years respectively.

**Problem 5 :**

The sum of the present ages of Kiran and Kate is 60 years. If the ratio of their present ages be 7 : 8, find their present age.

**Solution : **

Let 'x' and 'y' be the present ages of Kiran and Kate respectively.

**Given :** The ratio of the present ages of Kiran and Kate is

7 : 8

Then,

present age of Kiran = 7x

present age of Kate = 8x

**Given :** The sum of the present ages of Kiran and Kate is 60 years.

Then,

7x + 8x = 60

15x = 60

Divide each side by 15.

x = 4

Then,

7x = 7(4) = 28

8x = 8(4) = 32

So, the present ages of Kiran and Kate are 28 years and 32 years respectively.

**Problem 6 :**

Andrea is three times as old as her sister Anu. Three years ago, she was two years less than four times the age of her sister. Find their present ages.

**Solution : **

Let 'x' and 'y' be the present ages of Andrea and Anu respectively.

**Given :** Andrea is three times as old as her sister Anu.

x = 3y ----(1)

**Given :** Three years ago, Andrea was two years less than four times the age of her sister Anu.

Then,

x - 3 = 4(y - 3) - 2

x - 3 = 4y - 12 - 2

x - 3 = 4y - 14

Add 3 to each side.

x = 4y - 11 ----(2)

From (1) and (2),

3y = 4y - 11

Subtract 3y from each side.

0 = y - 11

Add 11 to each side.

11 = y

Substitute 11 for y in (1).

(1)----> x = 3(11)

x = 33

So, the present ages of Andrea and Anu are 33 years and 11 years respectively.

Apart from the stuff given above, if you need any other stuff in math, please use our google custom search here.

If you have any feedback about our math content, please mail us :

**v4formath@gmail.com**

We always appreciate your feedback.

You can also visit the following web pages on different stuff in math.

**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**

**Trigonometry word problems**

**Markup and markdown word problems **

**Word problems on mixed fractrions**

**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**