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Introduction

The topic of Problems with Ages is a frequent subject that is often found in exam papers. Candidates are tested on their capacity to work through complicated mathematical issues related to age calculation. The subject requires a solid knowledge of math concepts and the capability to apply them in a timed environment. This blog will explore the different kinds of Problems of age found in competitive examinations and offer tips and techniques to solve them effectively. Therefore, if you're trying to pass a competitive test and want to increase your ability to solve problems within this field, keep studying!

The Key Concepts and Terms for Age-related Issues

Knowing a few essential concepts and words can make answering them much easier in the case of age-related issues in exams. Let's explore them in an easy, casual manner.

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1. Current Age

It's just the current age of the person. A lot of queries revolve around this. It typically becomes the basis of formulas. Example: If the boy is now 12, he is twelve.

2. Age after 'x' years or Age 'x' Years Long

The terms you use can assist in shifting the timeline to either the left or right.

• Age after 5 years" means adding 5 years to your age.
• Age 10 years ago" means you subtract 10.
• This aids in formulating equations based on either past or future situations.

3. Age-related Difference

It is the permanent element of any age-related problem. The gap between two persons' ages is always unchanged as time passes.

Example: If the father of a child has a 25-year older than his son and he is 25 years younger in 10 years.

4. Ratio of Ages

Instead of numbers in actual form Ages are often provided in ratios such as 3:5.

Let's say the ages of A and B are 3:5, and the actual age is 5x and 3x. Based on that, create your formula.

5. Sum of Ages

You may be informed that two or more persons' ages will be a specific number. This sum is then utilized to create mathematical equations.

Example: If the average of a father's age and a son's age is 50 while the dad is two times older than the son, then use the following form:

x + 2x = 50 + 3x = 50 + the sum of x is 16.67 (son's the son's age)

When you've mastered the fundamental concepts and how they contribute to formulating equations, solving age-related problems will be less complicated.

Problems on Ages with solutions

Q1. The present age of Chandrika and Radha is approximately 3:4. Five years ago, the ratio of their age was 2:3. What is the current age of the Radha?

1. 12 years old
2. 15 years old
3. 20 years
4. Age: 22
5. 10 years

Answer:  (2) 15 Years Old

Solution:

Let the current age of the Radha be three times.

Let the current age of the Chandrika grow to 4x.

Five years ago, the age of Radha was (3x-5) years

Five years ago 5 years ago, the age of Chandrika is (4x-5)

In the context of the question (3x-5) : (4x-5) = 2:3

=(3x-5) / (4x-5) = 2/3

= 3(3x-5) = 2(4x-5)

= 9x - 15 = 8x - 10

=x = 5

Thus, the current rad age is 3x5, which equals 15 years.

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Q 2. If the age of Naksh and Shivani is twelve years older than the combined age of Shikhar Hari and Charu. Charu is precisely how many years older than Iqbal?

1. 11 years old
2. 13 years old
3. 15 years old
4. None of the above
5. Uncertainty in the determination

Answer : (4) none of the above

Solution:

Let the years of Naksh be x

Let the year of Shivani be y

Let Hari's age z

According to this question

(x+y) - (y+z) = 12

=x+y-y-z = 12

=x-z = 12

Therefore, Hari is 12 years older than Naksh

Q3. A father is two times older than his daughter. When 20 years ago his age was 10 times higher than his daughter's. What do you think is the age today for dad?

40 years 

32 years 

33 years

45 years

22 years

Answer: (4) 45 years

Solution:

Let the age of the father be 2x.

The present date of birth for the daughter = x

In response to the question

=2x-20 = 10(x-20)

=2x-20 = 10x - 200

=8x = 180

=x= 22.5

So, the current age of the father is 22.5 x 2, = 45 years.

Q4. Arun is 2 years older than Bharat, who is two times older than Charat. If the combined Ages of Arun, Bharat, and Charat are 27, what is the age of Bharat?

10 years

12 years

15 years

13 years

11 years

Answer: (1) 10 years

Solution:

Let the present age of Charat be x

Therefore, Bharat's current age is 2x

The age of Arun at present is 2+2x

In response to the question

x+2x+2+2x = 27

=5x+2 = 27

=5x=25

=x=5

The Bharat's Age = 2x5 = 10 years.

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Q 5. The average age of a mother and daughter is 56 years. After four years, the mother is three times as old as the daughter. What is the average age of the daughter as well as the mother?

1. 12 years, 41 years
2. 12 years, 30 years
3. 11 years, 34 years
4. 12 years, 44 years
5. 21 years, 42 years

Answer: (4) 12 years, 44 years

Solution:

Let the current mother's age be x old, and her age at present daughter be y.

Based on the answer, x+y =56-----(1)

At the age of 4 years, the age of the mother = x + 4.

Age of daughter after 4 years = y=4

So,

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

x+4 = 3y + 12

Based on this equation (1), we will get x = 56-y

Therefore, keeping the x value in equation 2, we will arrive at

(56-y) + 4 = 3y + 12

=60 - y = 3y + 12

=y = 12

The daughter's current age is 12 years old.

Her age at present is 56-12= 44 years.

Q6. What is the current age of Aman in 20 years, when his age is 10 times the age he was 10 years ago?

1. 6.2 years
2. 7.7 years
3. 13.3 year
4. 10 years 

Answer: (3) 13.3 year

Solution:

Let Aman's age now be the number x

Age of Aman before the age of 10 equals x + 10)

The age of Aman at 20 is (x + 20)

We know that their age of Aman after 20 years (x plus 20) is 10 times that of his age 10 years earlier (x 10-x)

Therefore, (x + 20) = 10 (x - 10)

After solving the equation, we obtain the formula: x + 20 =10x 100

9x equals 120 and x equals 13.3 years

Important Formulas

Below are a few equations associated with age-related issues which can help you to answer your questions more quickly and gain knowledge of the concept

• If you assume that the age at present is an x number, then the age at the end of n years would result in (x+n) Years.
• If you assume that the age at present is x that is, the age of the age of n will become (x-n) Years.
• If the date of birth is provided as the form of a ratio, like p:q, the age is regarded to be qx and px
• If you take the present age as the number x, then it is n times the age at present will equal (xxn) years.
• If you assume that your current age is one-in-n, the percentage of the age must be equivalent to (x/n) years.

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Tricks & Tips for Solving Age Problem

Here are a few useful tricks and techniques to aid you in learning to learn the most effective ways to solve problems on age in competitive examinations that are explained in a concise manner

1. Make use of Variables in an innovative way

• Make use of simple letters, such as "x," to indicate age that is not known.
• Future age for: x + years
• For older age: x - years
• Example For example: If A is 5 years younger than B, A = 5 + x B is 5x

2. Be aware that the age difference remains constant.

No matter what it's like just ten years ago or twenty years from now and beyond, the age difference never changes.

• Utilize this technique to remove incorrect alternatives rapidly.

3. Translate Words into Equations

Each age-related issue is the result of a disguised story. Look for phrases such as:

• "twice older," "years ago," "after 5 years", "sum of ages," and so on.
• Example: "A is twice as old as B after 5 years." 5 + A equals 2(B + 5.)

4. Training with Timelines

Make simple timelines when you're having trouble understanding historical or futuristic sources. This visually clarifies things!

5. Apply the Ratio Method when needed.

If you find ages in a ratio, you can interpret that they're the x value (e.g., 3x, 4x, 3x) to construct the equation using the sum of totals or differentiators.

6. Remove the use of options

Sometimes, backward solving by using options can save timeyou can plug in values to the conditions and check out what works!

7. Use Formula-Based Shortcuts to Practice (for fast solutions)

• If the total of ages is provided after the X-year mark, you can use: (Present total + No. of people x years) = future total age.
• Works best in group age problems!

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