# PROBLEMS ON AGEs

## About the topic problems on ages

Problems on ages play a major role in competitive exams like GMAT, GRE. There is no competitive exam without the questions from this topic. We have already learned this topic in our lower classes.Even though we have been already taught this topic in our lower classes, we need to learn some more short cuts which are being used to solve the problems in the above topic.

The only thing we have to do is, we need to apply the appropriate short cut and solve the problems in a limited time. This limited time will be one minute or less than one minute in most of the competitive exams.

## Why do students have to study this topic?

Students who are preparing to improve their aptitude skills and those who are preparing for this type of competitive test must prepare this topic in order to have better score. Because, today there is no competitive exam without questions from the topic problems on ages. Whether a person is going to write placement exam to get placed or a students is going to write a competitive exam in order to get admission in university, they must be prepared to solve problems on ages. This is the reason for why people must study this topic.

## Benefit of studying this topic

As we mentioned in the above paragraph, a person who wants to get placed in a company and a students who wants to get admission in university for higher studies must write competitive exams like placement test and entrance exam. To meet the above requirement, it is very important to score more marks in the above mentioned competitive exams. To score more marks, they have to prepare this topic. Preparing this topic would definitely improve their marks in the above exams. Preparing this topic is not difficult task. We are just going to remember the stuff that we have already learned in our lower classes

## How can students do time and work problems?

Students have to learn few basic operations in this topic time and work and some additional tricks. Already we are much clear with the four basic operations which we often use in math. They are addition, subtraction, multiplication and division. Even though we are much clear with these four basic operations, we have to be knowing some more stuff to do the problems which are being asked from this topic in competitive exams. The stuff which I have mentioned above is nothing but the tricks and shortcuts which need to solve the problems in a very short time.

## Shortcuts we use to solve the problems

Short cut is nothing but the easiest way to solve problems related to age. In competitive exams, we will have very limited time to solve each problem. Then only we will be able to attend all the questions. If we do problems in competitive exams in perfect manner with all the steps, it will definitely take much time and we may not able to attend the other questions. So we need some other way in which the problems can be solved in a very short time. The way we need to solve the problem quickly is called as shortcut.

Here, we are going to have some problems on ages . You can check your answer online and see step by step solution.

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.

 (A) 44 yrs                        (B) 45 yrs (C) 46 yrs                        (D) 47 yrs

jQuery UI Dialog functionality
Let "x" be the present age of the man and "y" be the sum of the present ages of two sons.

Present age of the man is 3 times the sum of the ages of 2 sons
x = 3y ------(1)

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)
x+5 = 2(y+10)
3y+5 = 2y+20........using equation(1)
Solving the above equation, we get y = 15

Plugging y=15 in equation(1),
x = 3(15)
x = 45 yrs

Hence the present age of the man is 45 years.

2. The 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.

 (A) 33 yrs                        (B) 34 yrs (C) 35 yrs                        (D) 36 yrs

jQuery UI Dialog functionality
Let "x" be the present age of the son.Then the present age of father is (3x+3)

3 years hence, father's age will be 10 years more than twice the age of the son
(3x+3)+3 = 2(x+3)+10
3x+6 = 2x+16
x = 10
To find the present age of the father, plug x = 10 in (3x+3)

Present age of the father = 3(10)+3 = 33 years

3. The ratio of the age of a man and his wife is 4:3. At the time of marriage the ratio was 5:3 and After 4 years this ratio will become 9:7. How many years ago were they married?

 (A) 12 yrs                        (B) 14 yrs (C) 16 yrs                        (D) 18 yrs

jQuery UI Dialog functionality
From the given ratio,age of the man is 4x and his wife is 3x
4 years hence, ratio of their ages is 9:7
(4x+4):(3x+4) = 9:7
7(4x+4):9(3x+4)
Solving the above equation, we get x = 8

Present age of the man = 4X8 = 32 yrs
Present age of the man = 3X8 = 24 yrs

Let them get married before "t" years from the present
for the above information, we have the ratio
(32-t):(24-t) = 5:3 (Because, at the time of marriage, their ages are in the ratio 5:3)
96-3t = 120-5t
Solve the above equation, we get t=12 years

Hence they got married 12 years before.

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?

 (A) 47 yrs                        (B) 48 yrs (C) 49 yrs                        (D) 50 yrs

jQuery UI Dialog functionality
Ten years ago, age of John and his father are x and 5x

Then, present age of John and his father are (x+10) and (5x+10)

John's age after six years will be three-seventh of his father's age
(x+10+6) = 3/7(5x+10+6)
(x+16) = 3/7(5x+16)
7(x+16) = 3(5x+16)
Solving the above equation, we get x=8

Present age of John's father = 5x+10
plug x = 8
Present age of John's father = 5(8)+10= 50 yrs

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?

 (A) 11 yrs                        (B) 12 yrs (C) 13 yrs                        (D) 14 yrs

jQuery UI Accordion - Default functionality
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 very clear that R is 12 years younger to P