Problems on Ages Tricks, Questions, Online Test, Video Lectures

Problems on ages is the part of Arithmetic Aptitude and important section of the competitive exam syllabus, to solve such questions, you are required the knowledge of linear equations. Sometimes it is easier to solve the questions by taking the given choices in account but this hit-and-trial method proves costly sometimes. Here we are giving you some easier as well as quicker way to solve this type of problems.

If the current age is x, then n times the age is nx.
If the current age is x, then age n years later/hence = x + n.
If the current age is x, then age n years ago = x - n.
The ages in a ratio a : b will be ax and bx.
If the current age is x, then $\frac{1}{n}$ of the age is $\frac{x}{n}$

Age Problems Involving A Single Person

Question: Five years ago, Arun’s age was half of the age he will be in 8 years. How old is he now?

Solution:
Step 1: Let x be Arun’s age now. Look at the question and put the relevant expressions above it.

Five year ago Arun's age: $x-5$
Arun’s age was half of the age he will be in 8 years: $\frac{1}{2}(x+8)$

Step 2: Write out the equation.

$x-5 = \frac{1}{2}(x+8)$

$x-5 = \frac{1}{2}x+4$

$x-5 = x-\frac{1}{2}x = 4 + 5$

$\frac{1}{2}x = 9$

$x = 18$

Answer: Arun is now 18 years old.

Age Problems Involving More Than One Person

Example 1

The age of the Mother 3 years ago was 7 times the age of his daughter. At present the Mother’s age is five times that of his son. What are the present ages of the Mother and the daughter?

Solution

Let the present age of daughter= x years.
Then, the present age of Mother= 5x years.
3 years ago,
7 (x – 3) = 5x – 3
or, 7x – 21 = 5x – 3
or, 2x = 18
∴ x = 9 years
Therefore, daughter’s age = 9 years.
Mother’s age = 45 years.

Example 2

The average age of Salman, Rishi, Akashy, Amit and Ritik is 28 years. The average age of Amit and Rtik is 25 years. What is the average age of Salman, Rishi and Akashy ?

Solutions:
Here 5 persons' average ( Salman, Rishi, Akashy, Amit and Ritik) age is = 28 Years.

That means their total age = 5 X 28 = 140 Years.

Similarly, average age of two persons (Amit and Ritik) is 25 years.So their total age = 25 X 2 = 50 Years.

here 140 years is the total age of 5 persons ( Salman, Rishi, Akashy, Amit and Ritik)
50 years is the total age of 2 persons (Amit and Ritik)

So, the total age of Salman, Rishi, Akashy = Total age of (Salman, Rishi, Akashy, Amit and Ritik) - Total age of Amit and Ritik)

= 140-50 = 90 years.

Average age of these 3 persons = 90/3 The average age of Salman, Rishi and Akashy = 30 Years

Example 3

At present the age of the Mother is five times that of the age of his son. Three years hence, the Mother’s age would be four times that of his son. Find the present ages of the Mother and the son.

Solution:

Let the present age of son = x years.
Then, the present age of father = 5x years.
3 years hence,
4(x + 3) = 5x + 3
or, 4x + 12 = 5x + 3
∴ x = 9 years.
Therefore, son’s age = 9 years and father’s age = 45 years.

Example 4

The ratio between the ages of Ram and Rohan is 5:8 respectively and difference between their ages after 5 years will be 12 years. What is the present age of Ram ?

Solution :
Usually for these type of questions students start with present age as X and adding 5 to get the ages after 5 years and later solve those equations. But its very time taking procedure.

A simple logic here is if the age difference between you and your friend is 8 years, after 5 or 10 years also the difference will be same.

the ratio between their ages is 5 : 8

That means their actual ages will be some 5X and 8X

Then the difference between their ages is 5X-8X
in this question it is given that the difference is 12 years

= 5X-8X = 12
= 3X=12 = X = 4

So obviously Ram's age = 5(4) = 20

Example 5

Yogesh is 30 years younger than his Father. Five years ago, Yogesh was 1/4 as old as his father was. How old is Yogesh today ?

Solution :

5 years ago the ratio between their ages was Yogesh : Mother = 1X : 4X

we know that Yogesh is 30 years younger than his mother. That means the difference between their ages is 30.

= 3X = 30
= X = 10.

But this is the age of 5 years ago. So, the present age will be = 10+5 = 15 Years

Problems on Ages Questions from Previous Year Exams

Problems on Age

Question 1 of 40

1. Question
Sushil was thrice as old as Sneha 6 years back. Sushil will be $\frac{5}{3}$ times as old as Sneha 6 years hence. How old is Sneha today?
- 18 years
- 12 years
- 22 years
- 24 years
Correct

Let Sneha age 6 years back = x.

Then, Sushil age 6 years back = 3x.

$\left(\frac{5}{3}\right)\times$ (x + 6 + 6) = (3x + 6 + 6)

Hence 5(x + 12) = 3(3x + 12) so x = 6.

Sneha today = (x + 6) years = 6 + 6 = 12 years.

Incorrect

Let Sneha age 6 years back = x.

Then, Sushil age 6 years back = 3x.

$\left(\frac{5}{3}\right)\times$ (x + 6 + 6) = (3x + 6 + 6)

Hence 5(x + 12) = 3(3x + 12) so x = 6.

Sneha today = (x + 6) years = 6 + 6 = 12 years.
Question 2 of 40

2. Question
The age of father 10 years ago was thrice the age of his son. Ten years hence, the father’s age will be twice that of his son. The ratio of their present ages is:
- 5:2
- 7:3
- 9:2
- 13:4
Correct

Let the ages of father and son 10 years ago be 3x and x years respectively.

Then, (3x + 10) + 10 = 2[(x + 10) + 10]

$\Rightarrow$ 3x + 20 = 2x + 40

$\Rightarrow$ x = 20.

Required ratio = (3x + 10) : (x + 10) = 70 : 30 = 7 : 3.

Incorrect

Let the ages of father and son 10 years ago be 3x and x years respectively.

Then, (3x + 10) + 10 = 2[(x + 10) + 10]

$\Rightarrow$ 3x + 20 = 2x + 40

$\Rightarrow$ x = 20.

Required ratio = (3x + 10) : (x + 10) = 70 : 30 = 7 : 3.
Question 3 of 40

3. Question
Ten years ago A was half of B in age. If the ratio of their present ages is 3 : 4, what will be the total of their present ages. [Bank P.O. 1991]
- 8 years
- 30 years
- 20years
- 35 years
Correct

Let As age 10 years ago = x.

Then, Bs age 10 years ago = 2x.

$\frac{x+10}{2x + 10}=\frac{3}{4}$ hence x = 5. Total of their present ages =(x + 10 + 2x + 10)
(3x + 20) = 35 years.

Incorrect

Let As age 10 years ago = x.

Then, Bs age 10 years ago = 2x.

$\frac{x+10}{2x + 10}=\frac{3}{4}$ hence x = 5. Total of their present ages =(x + 10 + 2x + 10)
(3x + 20) = 35 years.
Question 4 of 40

4. Question
The ratio of the ages of Meena and Meera is 4 : 3. The sum of their ages is 28 years. The ratio Of their ages after 8 years will be . [Central Excise ]
- 4:3
- 7:4
- 12:5
- 6 : 5
Correct

Let Meena age = 4x and Meera age = 3x.

Then, 4x + 3x = 28

$\Rightarrow$ 7x = 28

$\Rightarrow$ x = 4

Meena age = 16 years and Meera age = 12 years.

Ratio of their ages after 8 years = (16 + 8): (12 + 8) = 24 : 20 = 6 : 5.

Incorrect

Let Meena age = 4x and Meera age = 3x.

Then, 4x + 3x = 28

$\Rightarrow$ 7x = 28

$\Rightarrow$ x = 4

Meena age = 16 years and Meera age = 12 years.

Ratio of their ages after 8 years = (16 + 8): (12 + 8) = 24 : 20 = 6 : 5.
Question 5 of 40

5. Question
If 6 years are subtracted from the present age of Gulzar and the remainder is divided by 18, then the present age of his grandson Anup is obtained. If Anup is 2 years younger to Mahesh whose age is 5 years, then what is the present age of Gulzar . [Bank P.O. 1993]
- 96 years
- 48 years
- 84 years
- 60 years
Correct

Let Gulzar age are x years

Anups age =(5 - 2)years = 3 years.

Then $x-\frac{16}{18}=3$

$\Rightarrow$ x - 6 = 54

$\therefore$ x = 60

Incorrect

Let Gulzar age are x years

Anups age =(5 - 2)years = 3 years.

Then $x-\frac{16}{18}=3$

$\Rightarrow$ x - 6 = 54

$\therefore$ x = 60
Question 6 of 40

6. Question
Pushpa is twice as old as Rita was 2 years ago. If the difference of their ages be 2 years, how old is Pushpa today 7. [Railways 1991]
- 6 years
- 10 years
- 8 years
- 12 years
Correct

Let Rita age 2 years ago = x years.

Pushpa age now = 2x years.

2x - (x + 2) = 2 so x = 4.

Now Pushpas age = 2x = $2\times 4$ = 8 years

Incorrect

Let Rita age 2 years ago = x years.

Pushpa age now = 2x years.

2x - (x + 2) = 2 so x = 4.

Now Pushpas age = 2x = $2\times 4$ = 8 years
Question 7 of 40

7. Question
The total of the ages of A, B and C at present is 90 years. Ten years ago, the ratio of their ages was 1: 2: 3. What is the age of B at present?. [Bank P.O. 1993]
- 40 Years
- 20 Years
- 30 Years
- 18 Years
Correct

Let their ages 10 years ago is x, 2x and 3x years.

10 + 2x + 10 + 3x + 10 = 90

Therefore x = 10

B’s present age = (2x + 10) = $(2\times10+10)$ = 30 years.

Incorrect

Let their ages 10 years ago is x, 2x and 3x years.

10 + 2x + 10 + 3x + 10 = 90

Therefore x = 10

B’s present age = (2x + 10) = $(2\times10+10)$ = 30 years.
Question 8 of 40

8. Question
The ratio of the ages of Swati and Varun is 2: 5. After 8 years, their ages will be in the ratio of 1 : 2. The difference in their present ages (in years) is [C.B.1. 1993]
- 24
- 29
- 26
- 32
Correct

Let Swati age = 2Χ and Varuns age = 5Χ

$\Rightarrow \frac{2x+8}{5x+8}=\frac{1}{2}$

$\Rightarrow$ 2(2x + 8) = (5x + 8)

= 4x + 16 = 5x + 8

$\Rightarrow$ Χ = 8.

$\therefore$ Swati age = 16 years

and Varun age = 40 years

Difference of their ages = 24 years.

Swati age = 16 years and Varun age = 40 years.

Difference of their ages = 40 - 16 years = 24 years.

Incorrect

Let Swati age = 2Χ and Varuns age = 5Χ

$\Rightarrow \frac{2x+8}{5x+8}=\frac{1}{2}$

$\Rightarrow$ 2(2x + 8) = (5x + 8)

= 4x + 16 = 5x + 8

$\Rightarrow$ Χ = 8.

$\therefore$ Swati age = 16 years

and Varun age = 40 years

Difference of their ages = 24 years.

Swati age = 16 years and Varun age = 40 years.

Difference of their ages = 40 - 16 years = 24 years.
Question 9 of 40

9. Question
Jayesh is as much younger to Anil as he is oder to Prashant. If the sum of the ages of Anil and Prashant is 48 years, what is the age of Jayesh. [Bank P.O. 1991]
- 20
- 24
- 30
- none of these
Correct

Anil - Jayesh = Jayesh - prashant or Anil + Prashant =2 Jayesh .So 2 Jayesh = 48 or Jayesh = 24.

Incorrect

Anil - Jayesh = Jayesh - prashant or Anil + Prashant =2 Jayesh .So 2 Jayesh = 48 or Jayesh = 24.
Question 10 of 40

10. Question
A father is twice as old as his son. 20 years ago, the age of the father was 12 times the age of the son. The present age of the father (in years) is [Hotel Management]
- 44 years
- 22 years
- 32 years
- 45 years
Correct

Let sons age = Χ. Then, fathers age = 2x.

20 years ago the age are

12(x—20) = (2x - 20)

$\Rightarrow$ 12x - 240 = 2x - 20

$\Rightarrow$ 10x = 220

$\Rightarrow$ x = 22

Fathers present age = 2x = $2\times 22$ = 44 years.

Incorrect

Let sons age = Χ. Then, fathers age = 2x.

20 years ago the age are

12(x—20) = (2x - 20)

$\Rightarrow$ 12x - 240 = 2x - 20

$\Rightarrow$ 10x = 220

$\Rightarrow$ x = 22

Fathers present age = 2x = $2\times 22$ = 44 years.
Question 11 of 40

11. Question
Ratio of Ashok age to Sandeep age is 4 : 3. Ashok will be 26 years old after 6 years. How old is Sandeep now?. [Railways 1989]
- 12 years
- 19 years
- 15 years
- 21 years
Correct

The ratio of Ashok and Sandeep ages be 4x and 3x years.

Now 4x + 6 = 26 hence x = 5

so Age of Sandeep = 3x = $3\times 5$ = 15 years

Incorrect

The ratio of Ashok and Sandeep ages be 4x and 3x years.

Now 4x + 6 = 26 hence x = 5

so Age of Sandeep = 3x = $3\times 5$ = 15 years
Question 12 of 40

12. Question
One year ago, Mrs Promila was four times as old as her daughter Swati. Six years hence, Mrs Promilas age will exceed her daugther’s age by 9 years. The ratio of the present ages of Promila and her daughter is [C.B.I. 1993)
- 9 : 2
- 12 : 5
- 11 : 2
- 13 : 4
Correct

Let Swati age 1 year ago = x .

Then, Promila age 1 year ago = 4x .

(4x + 6) - ( x + 6) = 9 or x = 3.

Present age of Promila 4x + 1 = (12 + 1) years = 13 years.

Present age of Swati = (3 + 1) years = 4 years.

Ratio of their ages = 13 : 4.

Incorrect

Let Swati age 1 year ago = x .

Then, Promila age 1 year ago = 4x .

(4x + 6) - ( x + 6) = 9 or x = 3.

Present age of Promila 4x + 1 = (12 + 1) years = 13 years.

Present age of Swati = (3 + 1) years = 4 years.

Ratio of their ages = 13 : 4.
Question 13 of 40

13. Question
The sum of the ages of a father and son is 45 years. Five years ago, the product of their ages was four times the fathers age at that time. The present age of father and son, respectively are [Hotel Management]
- 25 years and 10 years
- 39 years and 6 years
- 36 years and 9 years
- None of these
Correct

Let sons age = x years

Then fathers age = (45 - Χ) years.

$\Rightarrow$ (Χ - 5)(45- Χ- 5) = 4(45 - Χ - 5)

$\Rightarrow$ (Χ - 5) = 4

Therefore Χ = 9

Their ages are 36 years and 9 years.

Incorrect

Let sons age = x years

Then fathers age = (45 - Χ) years.

$\Rightarrow$ (Χ - 5)(45- Χ- 5) = 4(45 - Χ - 5)

$\Rightarrow$ (Χ - 5) = 4

Therefore Χ = 9

Their ages are 36 years and 9 years.
Question 14 of 40

14. Question
Average age of A and B is 24 years and average age of B, C and D is 22 years. The sum of the ages of A, B, C and D is [Bank P.O. 1992]
- 90 years
- 114 years
- 96 years
- Data inadequate
Correct

A + B = (24 $\times$ 2) = 48 and B + C + D = (22 $\times$ 3) = 66

With this data, we can not find A + B + C + D.

So, the data is inadequate,

Incorrect

A + B = (24 $\times$ 2) = 48 and B + C + D = (22 $\times$ 3) = 66

With this data, we can not find A + B + C + D.

So, the data is inadequate,
Question 15 of 40

15. Question
In 10 years, A will be twice as old5as B was 10 years ago. If A is now 9 years older than B, the present age of B is[L.I.C. 1989]
- 19 years
- 29 years
- 39 years
- 49 years
Correct

Let B age = x years. Then, As age = (x + 9) years.

(x + 9 + 10) = 2(x - 10)

$\rightarrow$ x + 19 = 2x - 20

$\rightarrow$ x = 39

Present age of B = 39 years.

Incorrect

Let B age = x years. Then, As age = (x + 9) years.

(x + 9 + 10) = 2(x - 10)

$\rightarrow$ x + 19 = 2x - 20

$\rightarrow$ x = 39

Present age of B = 39 years.
Question 16 of 40

16. Question
The average age of 12 students is 20 years if the age of one more student is included, the average decreases by 1,What is the age of the new student?. [Bank P.O. 1991]
- 5 years
- 9 years
- 7 years
- 11 years
Correct

New average = (20 - 1) = 19.

Age of new student = (13 $\times$ 19 - 12 $\times$ 20) years = 7 years

Incorrect

New average = (20 - 1) = 19.

Age of new student = (13 $\times$ 19 - 12 $\times$ 20) years = 7 years
Question 17 of 40

17. Question
Sneha age is $\frac{1}{6^{th}}$ of her fathers age. Sneha fathers age will be twice of Vimal age after 10 years. If Vimal eighth birthday was celebrated two years before, then what is Sneha present age? [Bank P.O. 1992]
- 24 years
- 6 years
- 30 years
- 5 years
Correct

Vimal age after 10 years = (8 + 2 + 10) years = 20 years.

Sneha father’s age after 10 years = 40 years.

Sneha father’s present age = 30 years.

Sneha age= $\frac{1}{6}\times$ 30 years = 5 years.

Incorrect

Vimal age after 10 years = (8 + 2 + 10) years = 20 years.

Sneha father’s age after 10 years = 40 years.

Sneha father’s present age = 30 years.

Sneha age= $\frac{1}{6}\times$ 30 years = 5 years.
Question 18 of 40

18. Question
The average age of an adult class is 40 years. Twelve new students with an average age of 32 years join the class, thereby decreasing the average of the class by 4 years. The original strength of the class was. [Assistant Grade]
- 10
- 12
- 11
- 15
Correct

Let, original strength = x.

$\frac{40x + 12\times 32}{x + 12}$ = 36

$\Rightarrow 40x+384=36(x+12)$

$\Rightarrow$ 40x +384 = 36x + 432

$\Rightarrow$ 40x - 36x = 432 - 384

$\Rightarrow$ 4x = 48

$\Rightarrow$ x = 12

$\therefore$ original strength x = 12

Incorrect

Let, original strength = x.

$\frac{40x + 12\times 32}{x + 12}$ = 36

$\Rightarrow 40x+384=36(x+12)$

$\Rightarrow$ 40x +384 = 36x + 432

$\Rightarrow$ 40x - 36x = 432 - 384

$\Rightarrow$ 4x = 48

$\Rightarrow$ x = 12

$\therefore$ original strength x = 12
Question 19 of 40

19. Question
The ages of two persons differ by 20 years. If 5 years ago, the elder one be 5 times as old as the younger one, their present ages (in years) are respectively [N.D.A. 1994]
- 30, 10
- 29, 9
- 25, 5
- 50, 30
Correct

Let their ages be x and (x + 20) years.

5 year before the ages be 5 (x- 5) = (x + 20 - 5) $\Rightarrow$ 4x = 40 and x = 10.

Their present ages are 30 years and 10 years.

Incorrect

Let their ages be x and (x + 20) years.

5 year before the ages be 5 (x- 5) = (x + 20 - 5) $\Rightarrow$ 4x = 40 and x = 10.

Their present ages are 30 years and 10 years.
Question 20 of 40

20. Question
Ten years ago, Chandrawati s mother was four times older than her daughter. After ten years, the mother will be twice older than daughter. The present age of Chandrawati is [Bank P.O. 1990]
- 5 years
- 20 years
- 10 years
- 30 years
Correct

Let Chandrawatis age 10 years ago is x years.

Her mothers age 10 years ago 4x.

(4x + 10) + 10 = 2(x + 10 + 10) or 2x = 20 or x = 10.

Present age of Chandrawati (x + 10) = 20 years.

Incorrect

Let Chandrawatis age 10 years ago is x years.

Her mothers age 10 years ago 4x.

(4x + 10) + 10 = 2(x + 10 + 10) or 2x = 20 or x = 10.

Present age of Chandrawati (x + 10) = 20 years.
Question 21 of 40

21. Question
The ratio of Vimal age and Aruna age is 3 : 5 and the sum of their ages is 80 years. The ratio of their ages after 10 years will be [Bank P.O. 1990]
- 2 : 3
- 3 : 2
- 1 : 2
- 3 : 5
Correct

Let Vimal and Aruna ages be 3x and 5x years.

Then,3x + 5x = 80 so x = 10

Ratio of their ages after 10 years = (3x+ 10) : (5x+ 10)

40 : 60 = 2 : 3

Incorrect

Let Vimal and Aruna ages be 3x and 5x years.

Then,3x + 5x = 80 so x = 10

Ratio of their ages after 10 years = (3x+ 10) : (5x+ 10)

40 : 60 = 2 : 3
Question 22 of 40

22. Question
The ages of Ram and Mukta are in the ratio of 3 : 5. After 9 years, the ratio of their ages will becomes 3 :4. The present age of Mukta (in years) is. [Assistant Grade]
- 9 years
- 18 years
- 15 years
- 24 years
Correct

Let Ram age = 3x and Mukta age = 5x.

$\frac{3x+9}{5x+9}=\frac{3}{4}$

$\Rightarrow$ 4(3x + 9) = 3(5x + 9)

$\Rightarrow$ 12x + 36 = 15x + 27

$\Rightarrow$ -3x = -9

$\Rightarrow$ x = 3

Mukta age = 5x = $5\times 3$ = 15 years

Incorrect

Let Ram age = 3x and Mukta age = 5x.

$\frac{3x+9}{5x+9}=\frac{3}{4}$

$\Rightarrow$ 4(3x + 9) = 3(5x + 9)

$\Rightarrow$ 12x + 36 = 15x + 27

$\Rightarrow$ -3x = -9

$\Rightarrow$ x = 3

Mukta age = 5x = $5\times 3$ = 15 years
Question 23 of 40

23. Question
Mohit is younger than Sohit by 4 years. If their ages are in the respective ratio of 3 : 5, How old is Mohit ?
- 6 years
- 12 years
- 13 years
- 16 years
Correct

Let Sohit age be x years. then, Mohit age = (x - 4) years.

so, $\frac{x-4}{x}=\frac{3}{5}$

=> 5x - 20 = 3x

=> 5x - 3x = 20

=> 2x = 20

=> x = 10

Hence, Mohit age = (x- 4) = 10 - 6 = 6 years.

Incorrect

Let Sohit age be x years. then, Mohit age = (x - 4) years.

so, $\frac{x-4}{x}=\frac{3}{5}$

=> 5x - 20 = 3x

=> 5x - 3x = 20

=> 2x = 20

=> x = 10

Hence, Mohit age = (x- 4) = 10 - 6 = 6 years.
Question 24 of 40

24. Question
The ratio between the present ages of A and B is 3 : 5 respectively. If the difference between B's present age and A's after 7 year is 3 what is the total of A's and B's present age ?
- 10 years
- 30 years
- 40 years
- 45 years
Correct

Let the present A and B be 3x year and 5x year respectively.

Then, 5x - (3x + 7) = 3

$\Rightarrow$ 5x - 3x - 7 = 3.

$\Rightarrow$ 2x - 7 - 3 = 2x = 10

$\Rightarrow$ x = 5

$\therefore$ Required Sum = 3x + 5x = 8x = 8 $\times$ 5 = 40 years.

Incorrect

Let the present A and B be 3x year and 5x year respectively.

Then, 5x - (3x + 7) = 3

$\Rightarrow$ 5x - 3x - 7 = 3.

$\Rightarrow$ 2x - 7 - 3 = 2x = 10

$\Rightarrow$ x = 5

$\therefore$ Required Sum = 3x + 5x = 8x = 8 $\times$ 5 = 40 years.
Question 25 of 40

25. Question
At present the ratio between the ages of Rahul and Nirdosh is 2 : 1 after 7 years, Rahul age will be 21 years. what is the age of Nirdosh at present ?
- 5 years
- 7 years
- 9 years
- 12years
Correct

Let the present age of Rahul and Nirdosh be 2x and x years respectviely.

Then, 2x + 7 = 21

$\Rightarrow$ x = 7.

Nirdosh age is 7.

Incorrect

Let the present age of Rahul and Nirdosh be 2x and x years respectviely.

Then, 2x + 7 = 21

$\Rightarrow$ x = 7.

Nirdosh age is 7.
Question 26 of 40

26. Question
Present age of A and B are in the ratio of 6 : 7 respectively. 8 years hence, the ratio of ages will become 7 : 8 respectively. What is A's present age in years ?
- 30 years
- 40 years
- 48 years
- 52 years
Correct

Let the present ages of A and B be 6x and 7x years respectively.

$\frac{6x+8}{7x+8}=\frac{7}{8}$

=> 48x + 64 = 49x + 56

=> 64 - 56 = 49x - 48x

=> x = 8

So, A's present age = 6x = 6 × 8 = 48 years

Incorrect

Let the present ages of A and B be 6x and 7x years respectively.

$\frac{6x+8}{7x+8}=\frac{7}{8}$

=> 48x + 64 = 49x + 56

=> 64 - 56 = 49x - 48x

=> x = 8

So, A's present age = 6x = 6 × 8 = 48 years
Question 27 of 40

27. Question
The ratio ages of a man and his wife is 5 : 4. After six years, this ratio will be 4 : 3 at the time of marriage, the ratio was 7 : 5, then how many years ago were they married ?.
- 12 and 25 years
- 15 and 10 years
- 30 and 24 years
- None of these
Correct

Let the present ages of the man and his wife be 5x and 4x respectively.

Then , $\frac{5x+6}{4x+6}=\frac{4}{3}$

$\Rightarrow$ 15x + 18 = 16x + 24

$\Rightarrow$ x = 6

So, their present ages are 30 years and 24 years respectively.

Incorrect

Let the present ages of the man and his wife be 5x and 4x respectively.

Then , $\frac{5x+6}{4x+6}=\frac{4}{3}$

$\Rightarrow$ 15x + 18 = 16x + 24

$\Rightarrow$ x = 6

So, their present ages are 30 years and 24 years respectively.
Question 28 of 40

28. Question
The ratio between the present ages of X and Y is 3 : 2 respectively. the ratio between X's age 5 years ago and Y's age 5 years hence is 1 : 1. What is the ratio between X's 4 years hence and Y's 4 years ago ?
- 1 : 3
- 2 : 3
- 4 : 5
- 7 : 5
Correct

Let the present ages of X and Y be 3x and 2x year respectively.

$\Rightarrow \frac{3x-5}{2x-5}=\frac{1}{1}$

$\Rightarrow$ 3x - 5 = 2x - 5

$\Rightarrow$ x = 10

Therefore Required ratio = (3x + 5) : (3x - 5) = 35 : 25 = 7 : 5.

Incorrect

Let the present ages of X and Y be 3x and 2x year respectively.

$\Rightarrow \frac{3x-5}{2x-5}=\frac{1}{1}$

$\Rightarrow$ 3x - 5 = 2x - 5

$\Rightarrow$ x = 10

Therefore Required ratio = (3x + 5) : (3x - 5) = 35 : 25 = 7 : 5.
Question 29 of 40

29. Question
Two years ago a man was 6 times as old as his son. After 18 years, he will be twice as old as his son. Their present ages (in years) are. [N.D.A. 1992]
- 32,7
- 36, 11
- 34,9
- None of these
Correct

Let sons age 2 years ago be x.

Mans age 2 years ago = 6x.

2(x + 2 + 18) = (6x + 2 + 18) hence 4x = 20 so Χ = 5.

Their present ages are (6x + 2) and (x + 2) i.e. 32 years and 7 years.

Incorrect

Let sons age 2 years ago be x.

Mans age 2 years ago = 6x.

2(x + 2 + 18) = (6x + 2 + 18) hence 4x = 20 so Χ = 5.

Their present ages are (6x + 2) and (x + 2) i.e. 32 years and 7 years.
Question 30 of 40

30. Question
Kamla got married 6 years ago. Today her age is 1.25 times her age at the time of marriage. Her sons age is $\frac{1}{10}$ times her age. Her sons age is [Bank P.O. 1988]
- 2 years.
- 4 years.
- 3 years.
- 5 years.
Correct

Let Kamla age 6 years ago = x years.

Kamla present age = (x + 6) years.

x+6= $\frac{5}{4}\times$ x or x = 24.

Kamla present age= 30 years.
Sons present age = $\left (\frac{1}{10}\right)\times30$ years = 3 years.

Incorrect

Let Kamla age 6 years ago = x years.

Kamla present age = (x + 6) years.

x+6= $\frac{5}{4}\times$ x or x = 24.

Kamla present age= 30 years.
Sons present age = $\left (\frac{1}{10}\right)\times30$ years = 3 years.
Question 31 of 40

31. Question
The ratio between the present ages of A and B is 8 : 9. If B is 5 years old than A, what will be the ratio of the ages of A and B after 5 years.
- 1 : 3
- 2 : 3
- 9 : 10
- 10 : 13
Correct

Let A's age and B's age be 8x years and 9x years respectively

then, 9x - 8x = 5x $\Rightarrow$ x = 5.

$\therefore$ Required ratio = (8x + 5) : (9x + 5) = 45 : 50 = 9 : 10

Incorrect

Let A's age and B's age be 8x years and 9x years respectively

then, 9x - 8x = 5x $\Rightarrow$ x = 5.

$\therefore$ Required ratio = (8x + 5) : (9x + 5) = 45 : 50 = 9 : 10
Question 32 of 40

32. Question
The total ages of Ankit , Narendra and Satendra is 93 years. five years ago, the ratio of their ages was 2 : 3 : 4. What is the present age of Satendra?
- 21 years
- 32 years
- 41 years
- 53 years
Correct

Let the ages of Ankit, Narendra and Satendra 5 years ago be 2x, 3x and 4x years respectively.

Then, (2x + 5) + (3x +5) + (4x + 5) = 96

⇒ 9x + 15 = 96 ⇒ 9x = 81 ⇒ x = 9.

Therefore the present age of Satendra (4x + 5) = (4 $\times$ 9 + 5) = 41 years

Incorrect

Let the ages of Ankit, Narendra and Satendra 5 years ago be 2x, 3x and 4x years respectively.

Then, (2x + 5) + (3x +5) + (4x + 5) = 96

⇒ 9x + 15 = 96 ⇒ 9x = 81 ⇒ x = 9.

Therefore the present age of Satendra (4x + 5) = (4 $\times$ 9 + 5) = 41 years
Question 33 of 40

33. Question
The ratio of the present ages of two Friends is 2 : 3 and six years back, the ratio was 1 : 3. What will be the ratio of their ages after 4 years ?.
- 1 : 3
- 3 : 4
- 2 : 3
- 3 : 5
Correct

Let the present ages of the two Friends be 2x and 3x respectively.

$\frac{2x-6}{3x-6}=\frac{1}{3}$

$\Rightarrow$ 6x - 18 = 3x - 6 $\Rightarrow$ 3x = 12, x = 4

Therefore required ratio = (2x + 4) : (3x + 4) = 12 : 16 = 3 : 4.

Incorrect

Let the present ages of the two Friends be 2x and 3x respectively.

$\frac{2x-6}{3x-6}=\frac{1}{3}$

$\Rightarrow$ 6x - 18 = 3x - 6 $\Rightarrow$ 3x = 12, x = 4

Therefore required ratio = (2x + 4) : (3x + 4) = 12 : 16 = 3 : 4.
Question 34 of 40

34. Question
The ratio of the Mother's age to her daughter's age is 9 : 5. the product of their ages is 1125. the ratio of their ages after six years will be :
- 5 : 3
- 2 : 3
- 3 : 4
- 6 : 2
Correct

Let the present ages of Mother and daughter be 9x and 5x respectively.

$\Rightarrow 9x\times 5x=1125$

⇒ 45x² = 1125

⇒ x² = 25 and x = 5.

Therefore required ratio = (9x + 5) : (5x + 5) = 50 : 30 = 5 : 3

Incorrect

Let the present ages of Mother and daughter be 9x and 5x respectively.

$\Rightarrow 9x\times 5x=1125$

⇒ 45x² = 1125

⇒ x² = 25 and x = 5.

Therefore required ratio = (9x + 5) : (5x + 5) = 50 : 30 = 5 : 3
Question 35 of 40

35. Question
The sum of the ages of A, B and C is 96 years. To find out B’s age, which of the following information given in the statements P and Q is/are sufficient
P : A is 6 years older than C
Q : The total of B and C’s ages is 56 years [Bank P.O. 1994]
- p
- both P and Q
- Q
- None of these
Correct

A + B + C = 96. Let C = Χ. Then, A = Χ + 6.

Χ + 6 + B + X = 96 so B + 2Χ = 90

Now B + C = 56 so B+ X = 56

Χ=(90 - 56) = 34.

B+2x = 90 => B = (90 - 68) = 22.

Thus both P and Q are needed.

Incorrect

A + B + C = 96. Let C = Χ. Then, A = Χ + 6.

Χ + 6 + B + X = 96 so B + 2Χ = 90

Now B + C = 56 so B+ X = 56

Χ=(90 - 56) = 34.

B+2x = 90 => B = (90 - 68) = 22.

Thus both P and Q are needed.
Question 36 of 40

36. Question
Sachin was twice as old as Ajay 10 years back. How old is Ajay today if Sachin will be 40 years old 10 years hence?. [Bank P.O. 1991]
- 20 years
- 10 years
- 5 years
- 15years
Correct

Sachins age today = 30 years.
Sachins age 10 years back = 20 years.
Ajays age 10 years back = 10 years.
Ajays age today =20 years.

Incorrect

Sachins age today = 30 years.
Sachins age 10 years back = 20 years.
Ajays age 10 years back = 10 years.
Ajays age today =20 years.
Question 37 of 40

37. Question
The ages of two persons differ by 20 years. If 5 years ago, the elder one be 5 times as old as the younger one, their present ages (in years) are respectively :. [N.D.A. 1994]
- 30, 10
- 29, 9
- 25, 5
- 50, 30
Correct

Let their ages be x and (x + 20) years.
5 (x- 5) = (x + 20 - 5) or 4x = 40 or x = 10.
Their present ages are 30 years and 10 years.

Incorrect

Let their ages be x and (x + 20) years.
5 (x- 5) = (x + 20 - 5) or 4x = 40 or x = 10.
Their present ages are 30 years and 10 years.
Question 38 of 40

38. Question
Five years ago the ratio of the ages of Omkar and Nitin was 8 : 7. Three years hence, the ratio of their ages will be 11 : 10. what is Nitin's age at present?
- 12 years
- 15 years
- 17 years
- 19 years
Correct

Let the Omkar and Nitin age Five years ago = 8x and 7x.

$\frac{(8x + 5)+3}{(7x +5)+ 3} =\frac{12}{11}$

⇒ 88x +88 = 84x + 96
⇒ 4x = 8 ⇒ x = 2. Nitin's present age = (7x + 5) = (7 × 2 + 5) = 19 years.

Incorrect

Let the Omkar and Nitin age Five years ago = 8x and 7x.

$\frac{(8x + 5)+3}{(7x +5)+ 3} =\frac{12}{11}$

⇒ 88x +88 = 84x + 96
⇒ 4x = 8 ⇒ x = 2. Nitin's present age = (7x + 5) = (7 × 2 + 5) = 19 years.
Question 39 of 40

39. Question
The present ages of three colleague's are in proportions 3 : 5 : 7. Four years ago, the sum of thier ages was 48. find thier present ages (in years) ?.
- 12 , 20 and 28 years
- 12 , 30 and 38 years
- 11 , 15 and 20 years
- 22, 25and 28 years
Correct

Let the present age of three colleague's are : 3x, 5x and 7x

(3x - 4) + (5x - 4) + (7x - 4) = 48.

15x - 12 = 48 ⇒ 15x = 60 ⇒ x = 4.

Their present ages are 12 years, 20 years and 28 years respectively.

Incorrect

Let the present age of three colleague's are : 3x, 5x and 7x

(3x - 4) + (5x - 4) + (7x - 4) = 48.

15x - 12 = 48 ⇒ 15x = 60 ⇒ x = 4.

Their present ages are 12 years, 20 years and 28 years respectively.
Question 40 of 40

40. Question
Rahul is as much younger than Mukesh as he is older than Lata. If the sum of the ages of Mukesh and Lata is 60 years, what is definitely the difference between Mukesh and Rahul's age ?
- 20 years
- 24 years
- Can't be determined
- None of these
Correct

Can't be determined

Incorrect

Can't be determined