1. If the current age is x, then n times the age is nx.
2. If the current age is x, then age n years later/hence = x + n.
3. If the current age is x, then age n years ago = x – n.
4. The ages in a ratio a : b will 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?
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:
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?
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?
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:
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?
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?
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?
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:
Average age of employees working in a department is 30 years. In the next year, ten workers will retire. What will be the average age in the next year?
Thus, I and II both together give the answer. So, correct answer is (E).
Answer:17 Option E
Explanation:
I. Retirement age is 60 years.
II. 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).
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8
3
5
Age of the youngest child = 
2
Son’s age 5 years back (19 – 5) = 14 years.
(2
5
9(5
45
45
Anand’s present age = 4
(
10(6
5
Sagar’s present age = (5
54 – 
6
Son’s age after 6 years = (
4
Deepak’s age = 3
9
2
20
Their present ages are 4
Required difference = (42 – 36) years = 6 years.
2(2
3
Required ratio = (3
D =
S = 25D – 120 ….(ii)
4S = 120.
S = 30.
D – 2S = 0 ….(i)
5D – 9S = 20 ….(iv)
D – 3S = -20 ….(v)
I alone as well as II alone give the answer. Hence, the correct answer is (C).