Age Problems
Important Formulas on “Problems on Ages”:
- If the current age is x, then ntimes the age is nx.
- If the current age is x, then age nyears later/hence = x+ n.
- If the current age is x, then age nyears ago = x– n.
- The ages in a ratio a: bwill be ax and bx.
| 5. If the current age is x, then | 1 | of the age is | x | . |
| n | n |
Example:
A problem with one variable: How old is Al?
Many single-variable algebra word problems have to do with the relations between different people’s ages. For example:
Al’s father is 45. He is 15 years older than twice Al’s age. How old is Al?
We can begin by assigning a variable to what we’re asked to find. Here this is Al’s age, so let Al’s age = x.
We also know from the information given in the problem that 45 is 15 more than twice Al’s age. How can we translate this from words into mathematical symbols? What is twice Al’s age?
Well, Al’s age is x, so twice Al’s age is 2x, and 15 more than twice Al’s age is 15 + 2x.That equals 45, right? Now we have an equation in terms of one variable that we can solve for x: 45 = 15 + 2x.
| original statement of the problem: | 45 = 15 + 2x |
| subtract 15 from each side: | 30 = 2x |
| divide both sides by 2: | 15 = x |
Since x is Al’s age and x = 15, this means that Al is 15 years old.
It’s always a good idea to check our answer:
| twice Al’s age is 2 x 15: | 30 |
| 15 more than 30 is 15 + 30: | 45 |
This should be the age of Al’s father, and it is.
Questions:
Level-I:
| 1. | Father is aged three times more than his son Ronit. After 8 years, he would be two and a half times of Ronit’s age. After further 8 years, how many times would he be of Ronit’s age? | |||||||||||||||
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| 2. | The sum of ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child? | |||||||
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| 3. | A father said to his son, “I was as old as you are at the present at the time of your birth”. If the father’s age is 38 years now, the son’s age five years back was: | |||||||
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| 4. | A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 27, the how old is B? | |||||||||
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| 5. | Present ages of Sameer and Anand are in the ratio of 5 : 4 respectively. Three years hence, the ratio of their ages will become 11 : 9 respectively. What is Anand’s present age in years? | |||||||||
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| 6. | A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is: | |||||||
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| 7. | Six years ago, the ratio of the ages of Kunal and Sagar was 6 : 5. Four years hence, the ratio of their ages will be 11 : 10. What is Sagar’s age at present? | |||||||||
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| 8. | The sum of the present ages of a father and his son is 60 years. Six years ago, father’s age was five times the age of the son. After 6 years, son’s age will be: | |||||||
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| 9. | At present, the ratio between the ages of Arun and Deepak is 4 : 3. After 6 years, Arun’s age will be 26 years. What is the age of Deepak at present ? | |||||||
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| 10. | Sachin is younger than Rahul by 7 years. If their ages are in the respective ratio of 7 : 9, how old is Sachin? | |||||||||
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11. |
Level-II:
The present ages of three persons in proportions 4 : 7 : 9. Eight years ago, the sum of their ages was 56. Find their present ages (in years). |
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| 12. | Ayesha’s father was 38 years of age when she was born while her mother was 36 years old when her brother four years younger to her was born. What is the difference between the ages of her parents? | |||||||
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| 13. | A person’s present age is two-fifth of the age of his mother. After 8 years, he will be one-half of the age of his mother. How old is the mother at present? | |||||||
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| 14. | Q is as much younger than R as he is older than T. If the sum of the ages of R and T is 50 years, what is definitely the difference between R and Q’s age? | |||||||||
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| 15. | The age of father 10 years ago was thrice the age of his son. Ten years hence, father’s age will be twice that of his son. The ratio of their present ages is: | |||||||
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Answers:
Level-I:
Answer:1 Option A
Explanation:
Let Ronit’s present age be x years. Then, father’s present age =(x + 3x) years = 4x years.
| (4x + 8) = | 5 | (x + 8) | |
| 2 |
8x + 16 = 5x + 40
3x = 24
x = 8.
| Hence, required ratio = | (4x + 16) | = | 48 | = 2. |
| (x + 16) | 24 |
Answer:2 Option A
Explanation:
Let the ages of children be x, (x + 3), (x + 6), (x + 9) and (x + 12) years.
Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50
5x = 20
x = 4.
Age of the youngest child = x = 4 years.
Answer:3 Option A
Explanation:
Let the son’s present age be x years. Then, (38 – x) = x
2x = 38.
x = 19.
Son’s age 5 years back (19 – 5) = 14 years.
Answer:4 Option D
Explanation:
Let C’s age be x years. Then, B’s age = 2x years. A’s age = (2x + 2) years.
(2x + 2) + 2x + x = 27
5x = 25
x = 5.
Hence, B’s age = 2x = 10 years.
Answer:5 Option A
Explanation:
Let the present ages of Sameer and Anand be 5x years and 4x years respectively.
| Then, | 5x + 3 | = | 11 |
| 4x + 3 | 9 |
9(5x + 3) = 11(4x + 3)
45x + 27 = 44x + 33
45x – 44x = 33 – 27
x = 6.
Anand’s present age = 4x = 24 years.
Answer:6 Option D
Explanation:
Let the son’s present age be x years. Then, man’s present age = (x + 24) years.
(x + 24) + 2 = 2(x + 2)
x + 26 = 2x + 4
x = 22.
Answer:7 Option A
Explanation:
Let the ages of Kunal and Sagar 6 years ago be 6x and 5x years respectively.
| Then, | (6x + 6) + 4 | = | 11 |
| (5x + 6) + 4 | 10 |
10(6x + 10) = 11(5x + 10)
5x = 10
x = 2.
Sagar’s present age = (5x + 6) = 16 years.
Answer:8 Option D
Explanation:
Let the present ages of son and father be x and (60 –x) years respectively.
Then, (60 – x) – 6 = 5(x – 6)
54 – x = 5x – 30
6x = 84
x = 14.
Son’s age after 6 years = (x+ 6) = 20 years..
Answer:9 Option B
Explanation:
Let the present ages of Arun and Deepak be 4x years and 3x years respectively. Then,
4x + 6 = 26 4x = 20
x = 5.
Deepak’s age = 3x = 15 years.
Answer:10 Option D
Explanation:
Let Rahul’s age be x years.
Then, Sachin’s age = (x – 7) years.
| x – 7 | = | 7 | |
| x | 9 |
9x – 63 = 7x
2x = 63
x = 31.5
Hence, Sachin’s age =(x – 7) = 24.5 years.
Answer:11 Option B
Explanation:
Let their present ages be 4x, 7x and 9x years respectively.
Then, (4x – 8) + (7x – 8) + (9x – 8) = 56
20x = 80
x = 4.
Their present ages are 4x = 16 years, 7x = 28 years and 9x = 36 years respectively.
Answer:12 Option C
Explanation:
Mother’s age when Ayesha’s brother was born = 36 years.
Father’s age when Ayesha’s brother was born = (38 + 4) years = 42 years.
Required difference = (42 – 36) years = 6 years.
Answer:13 Option C
Explanation:
Let the mother’s present age be x years.
| Then, the person’s present age = | 2 | x | years. | ||
| 5 |
| 2 | x + 8 | = | 1 | (x + 8) | |||
| 5 | 2 |
2(2x + 40) = 5(x + 8)
x = 40.
Answer:14 Option D
Explanation:
Given that:
1. The difference of age b/w R and Q = The difference of age b/w Q and T.
2. Sum of age of R and T is 50 i.e. (R + T) = 50.
Question: R – Q = ?.
Explanation:
R – Q = Q – T
(R + T) = 2Q
Now given that, (R + T) = 50
So, 50 = 2Q and therefore Q = 25.
Question is (R – Q) = ?
Here we know the value(age) of Q (25), but we don’t know the age of R.
Therefore, (R-Q) cannot be determined.
Answer:15 Option B
Explanation:
Let the ages of father and son 10 years ago be 3x and x years respectively.
Then, (3x + 10) + 10 = 2[(x + 10) + 10]
3x + 20 = 2x + 40
x = 20.
Required ratio = (3x + 10) : (x + 10) = 70 : 30 = 7 : 3.
Answer:16 Option E
Explanation:
| I. S = 5D D = | S | ….(i) |
| 5 |
- S – 5 = 25 (D – 5) S = 25D – 120 ….(ii)
| Using (i) in (ii), we get S = | 25 x | S | – 120 | ||
| 5 |
4S = 120.
S = 30.
Thus, I and II both together give the answer. So, correct answer is (E).
Answer:17 Option E
Explanation:
- Retirement age is 60 years.
- There are 50 employees in the department.
Average age of 50 employees = 30 years.
Total age of 50 employees = (50 x 30) years = 1500 years.
Number of employees next year = 40.
Total age of 40 employees next year (1500 + 40 – 60 x 10) = 940.
| Average age next year = | 940 | years = 23 | 1 | years. |
| 40 | 2 |
Thus, I and II together give the answer. So, correct answer is (E).
Answer:18 Option C
Explanation:
Let Divya’s present age be D years and Shruti’s present age b S years
Then, D = 2 x S D – 2S = 0 ….(i)
| I. | D + 5 | = | 9 | ….(ii) |
| S + 5 | 5 |
| II. | D – 10 | = | 3 | ….(iii) |
| S – 10 | 1 |
From (ii), we get : 5D + 25 = 9S + 45 5D – 9S = 20 ….(iv)
From (iii), we get : D – 10 = 3S – 30 D – 3S = -20 ….(v)
Thus, from (i) and (ii), we get the answer.
Also, from (i) and (iii), we get the answer.
I alone as well as II alone give the answer. Hence, the correct answer is (C).,
Age is a complex concept that has been studied by philosophers, scientists, and laypeople for centuries. There are many different ways to define age, and the meaning of age can vary depending on the context. In general, age is a measure of the passage of time, and it is often used to refer to the length of a person’s life. However, age can also be used to refer to the stage of life that a person is in, or to the level of maturity or experience that a person has.
Age difference is the difference in age between two people. Age progression is the process of getting older, and age regression is the process of getting younger. Age reversal is the process of reversing the aging process. Ageing is the process of physical and mental changes that occur as a person gets older. Longevity is the length of time that a person lives. Lifespan is the maximum length of time that a person can live. Senescence is the process of decline in physical and mental function that occurs as a person gets older. Gerontology is the study of the aging process. Geriatrics is the branch of medicine that deals with the care of older adults. Anti-ageing is the practice of delaying or preventing the aging process. Rejuvenation is the process of making someone or something look or feel younger. Immortality is the state of being alive forever.
The aging process is a complex and multifaceted process that is influenced by a variety of factors, including genetics, Environment, and lifestyle. The aging process is characterized by a number of changes, including a decline in physical function, a decrease in cognitive function, and an increase in the risk of chronic diseases.
There are a number of theories about why we age. One theory is that aging is caused by the accumulation of damage to cells and Tissues over time. Another theory is that aging is caused by a decline in the production of HORMONES and other substances that are essential for Health.
There is no one-size-fits-all answer to the question of how to age well. However, there are a number of things that people can do to improve their chances of aging well, including eating a healthy diet, exercising regularly, getting enough sleep, and managing Stress.
The prospect of age reversal has long been a source of fascination and hope. The idea of being able to turn back the clock and regain the vitality and health of youth is one that has captured the imagination of people for centuries. In recent years, there has been a growing interest in the possibility of age reversal, as scientific advances have begun to shed Light on the mechanisms of aging and the potential for interventions to slow or reverse the aging process.
There are a number of different approaches to age reversal that are currently being explored. One approach is to target the biological mechanisms that are thought to be responsible for aging. This includes interventions such as gene therapy, stem cell therapy, and the use of drugs that can modulate the activity of genes or proteins involved in aging. Another approach is to focus on the symptoms of aging, such as age-related diseases and frailty. This includes interventions such as lifestyle changes, such as diet and exercise, and the use of drugs that can treat age-related diseases.
The potential benefits of age reversal are significant. Age reversal could lead to a longer, healthier, and more productive life. It could also help to reduce the burden of age-related diseases and disabilities. However, there are also a number of potential risks associated with age reversal. These include the possibility of unintended side effects, the potential for ethical and social concerns, and the cost of such interventions.
Overall, the prospect of age reversal is a complex one. There are both potential benefits and risks associated with this approach. It is important to weigh the potential benefits and risks carefully before pursuing age reversal.
Here are some frequently asked questions and short answers about the following topics:
- What is the meaning of life?
The meaning of life is a question that has been asked by philosophers and theologians for centuries. There is no one answer that will satisfy everyone, but some possible answers include: to find happiness, to make a difference in the world, to learn and grow, and to connect with others.
- What is the purpose of life?
The purpose of life is another question that has been pondered by many people. Some believe that the purpose of life is to find happiness, while others believe that it is to make a difference in the world. Still others believe that the purpose of life is to learn and grow, or to connect with others.
- What is the best way to live a good life?
There is no one answer to this question, as what constitutes a good life will vary from person to person. However, some possible ingredients for a good life include: happiness, fulfillment, purpose, meaning, and connection with others.
- What is the difference between happiness and fulfillment?
Happiness is a feeling of joy or contentment, while fulfillment is a sense of satisfaction or accomplishment. Happiness is often fleeting, while fulfillment can be more lasting. Happiness can be derived from external sources, such as material possessions or experiences, while fulfillment is often derived from internal sources, such as personal Growth or relationships.
- What is the difference between success and happiness?
Success is often defined as the achievement of one’s goals, while happiness is a state of well-being or contentment. Success can be measured in many ways, such as financial success, career success, or personal success. Happiness is often more difficult to measure, but it can be felt in many ways, such as feeling joy, contentment, or satisfaction. Success and happiness are not always correlated. It is possible to be successful but not happy, and it is also possible to be happy but not successful.
- What is the difference between love and infatuation?
Love is a deep feeling of affection and care for another person, while infatuation is a short-lived feeling of intense attraction. Love is often based on shared values, interests, and experiences, while infatuation is often based on physical attraction. Love can be a lasting and fulfilling emotion, while infatuation is often fleeting.
- What is the difference between friendship and companionship?
Friendship is a relationship between two people who share a mutual affection and respect, while companionship is a relationship between two people who enjoy spending time together. Friendship is often based on shared interests and values, while companionship is often based on shared activities and experiences. Friendship can be a lasting and fulfilling relationship, while companionship is often more casual.
- What is the difference between fear and anxiety?
Fear is a natural response to danger, while anxiety is a feeling of worry or unease that is often unfounded. Fear is often based on a real or perceived threat, while anxiety is often based on irrational thoughts or beliefs. Fear can be a helpful emotion that can protect us from harm, while anxiety can be a debilitating emotion that can interfere with our daily lives.
- What is the difference between stress and anxiety?
Stress is a physical and mental reaction to a demanding situation, while anxiety is a feeling of worry or unease that is often unfounded. Stress can be caused by both positive and negative events, while anxiety is often caused by negative events. Stress can be a positive force that can motivate us to achieve our goals, while anxiety can be a negative force that can interfere with our daily lives.
- What is the difference between depression and sadness?
Depression is a mental illness that is characterized by feelings of sadness, hopelessness, and worthlessness, while sadness is a normal human emotion that is often caused by disappointment, loss, or grief. Depression is a serious condition that can interfere with our daily lives, while sadness is a temporary emotion that usually passes on its own.
- What is the difference between anger and rage?
Anger is a natural emotion that is often caused by a perceived threat or injustice, while rage is a more intense form of anger that is often accompanied by feelings of hatred and violence. Anger can be a healthy emotion that can motivate us to take action, while rage can be a destructive emotion that can harm ourselves and others.
- What is the difference between forgiveness and forgetting?
Forgiveness is the act of letting go of anger and resentment towards someone who has wronged us, while forgetting is the act of removing something from our memory. Forgiveness is a conscious choice that we make, while forgetting is a passive process that happens over time. Forgiveness can be a healing process that can help us move on from the past, while forgetting can be a way of protecting ourselves from future hurt.
Sure. Here are some multiple choice questions on the following topics:
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Time
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What is the difference between 12:00 AM and 12:00 PM?
(A) 12 hours
(B) 24 hours
(C) 0 hours
(D) 6 hours -
If it is 10:00 AM in New York, what time is it in London?
(A) 2:00 PM
(B) 3:00 PM
(C) 4:00 PM
(D) 5:00 PM -
If it is 12:00 AM on January 1st in New York, what time is it on January 1st in Los Angeles?
(A) 9:00 PM
(B) 10:00 PM
(C) 11:00 PM
(D) 12:00 AM -
Distance
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If you drive at 60 miles per hour for 2 hours, how far will you travel?
(A) 120 miles
(B) 180 miles
(C) 240 miles
(D) 300 miles -
If you walk at 3 miles per hour for 3 hours, how far will you travel?
(A) 9 miles
(B) 12 miles
(C) 15 miles
(D) 18 miles -
If you fly at 500 miles per hour for 2 hours, how far will you travel?
(A) 1000 miles
(B) 1500 miles
(C) 2000 miles
(D) 2500 miles -
Speed
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If you drive 60 miles in 2 hours, what is your average speed?
(A) 30 miles per hour
(B) 40 miles per hour
(C) 50 miles per hour
(D) 60 miles per hour -
If you walk 3 miles in 1 hour, what is your average speed?
(A) 3 miles per hour
(B) 6 miles per hour
(C) 9 miles per hour
(D) 12 miles per hour -
If you fly 500 miles in 2 hours, what is your average speed?
(A) 250 miles per hour
(B) 500 miles per hour
(C) 750 miles per hour
(D) 1000 miles per hour -
If you earn $10 per hour and work 40 hours per week, how much money will you earn in a week?
(A) $400
(B) $800
(C) $1200
(D) $1600 -
If you buy a car for $20,000 and sell it for $15,000, how much money did you lose?
(A) $5000
(B) $10,000
(C) $15,000
(D) $20,000 -
If you invest $1000 at 5% interest for 1 year, how much money will you have at the end of the year?
(A) $1050
(B) $1100
(C) $1150
(D) $1200
I hope these questions were helpful. Let me know if you have any other questions.