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The respective ages of father and his son are 41 and 16 years. In how many years will the father be twice as old as his son?

A.

9

B.

19

C.

15

D.

13

Answer with explanation

Answer: Option AExplanation

Suppose x years later the father will be twice as old as his son.

Then, x + 41 = 2 (x + 16)

⇒ x = 41 – 32 = 9 years

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The present ages of two persons are 36 and 50 yr, respectively. If after n yr the ratio of their ages will be 3: 4, then the value of n is?

A.

3

B.

5

C.

6

D.

7

Answer with explanation

Answer: Option CExplanation

According to the question,

(36 + n) / (50 + n) = 3/4

⇒ 144 + 4n = 150 + 3n

∴ n = 6

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Ten years ago, a man was seven times as old as his son. Two years hence, twice his age will be equal to five times the age of his son. What is the present age of the son?

A.

12

B.

13

C.

15

D.

14

Answer with explanation

Answer: Option DExplanation

Let son’s age 10 years ago be x years.

Then, man’s age 10 years ago = 7 years

Son’s present age = (x + 10) years,

Man’s present age = (7x + 10) years

∴2[(7x+10)+2] = 5[(x+10)+2]⇒2(7x+12)=5(x+12)⇒14x+24=5x+60⇒9x=36⇒x=4∴2[(7x+10)+2] = 5[(x+10)+2]⇒2(7x+12)=5(x+12)⇒14x+24=5x+60⇒9x=36⇒x=4

Son’s present age = (x + 10) years

= (4 + 10) years

= 14 years

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Father’s age today is three times as his daughter’s. After 10 years it would be just twice. What is the daughter’s age today?

A.

9

B.

10

C.

12

D.

15

Answer with explanation

Answer: Option BExplanation

Let, today’s age of the daughter = ‘A’ years.

Mom’s age today = 3A years

After 1 decade,

3A + 10 = 29A + 10

=> A = 10 years

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**Meena’s present age is three times her son’s present age and two fifth of her father’s present age. The average present age of all of them is 46 years. What is the difference between the Meena’s son’s present age and Meena’s father’s present age?**

A.

56

B.

78

C.

64

D.

58

Answer with explanation

Answer: Option BExplanation

The ratio of present age of Meena and her son’s age = 3 : 1 (3x, x)

Meena’s present age = (2/5)*Meena’s father’s present age

Meena’s father’s present age = (15/2)x

According to the question,

x + 3x + (15/2) x = 138

(2x + 6x + 15x)/2 = 138

23x = 138*2

x = 12

Required difference = 90 – 12 = 78 years

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The age of father 1010 years ago was thrice the age of his son. Ten years hence, the father’s age will be twice that of his son. What is the ratio of their present ages?

A.

7:3

B.

3:7

C.

4:9

D.

9:4

Answer with explanation

Answer: Option AExplanation

Let age of the son before 1010 years =x=x and

age of the father before 1010 years =3x=3x

(3x+20)=2(x+20)⇒x=20(3x+20)=2(x+20)⇒x=20

Age of the son at present =x+10=20+10=30=x+10=20+10=30

Age of the father at present =3x+10=3×20+10=70=3x+10=3×20+10=70

Required ratio =70:30=7:3

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At present, Kavita is twice Sarita’s age. 8 yr hence, the respective ratio between Kavita’s and Sarita’s ages will be 22 : 13. What is Kavita ‘s present age

A.

26 yr

B.

18 yr

C.

42 yr

D.

36 yr

Answer with explanation

Answer: Option DExplanation

Let Sarita;s present age = k yr

Then, Kavita’s present age = 2k yr

According to the question,

(2k + 8) / (k + 8) = 22/13

⇒ 26k + 104 = 22k + 176

⇒ 4k = 72

∴ k = 18

Hence, Kavita’s age = 2 x 18 = 36 yr

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The ages of 10 students and their teacher are such that the average of first 7 student’s age is 15 years; an average of the last three student’s age is 11 years. The average age of all the students and their teacher together is 15 years. Find the age of the teacher.

A.

24 years

B.

27 years

C.

30 years

D.

33 years

Answer with explanation

Answer: Option BExplanation

The sum of the ages of students and teachers =11*15=165

The sum of first seven students age=7*15=105

The sum of last three students age=3*11=33

The sum of age of 10 students =105+33=138

Teacher age =165-138=27years

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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

A.

15

B.

25

C.

45

D.

35

Answer with explanation

Answer: Option DExplanation

Let A’s age 10 years ago = x years.

Then, B’s age 10 years ago = 2x years.

(x + 10) / (2x+ l0) = 3/4

=> x = 5.

So, the total of their present ages =(x + 10 + 2x + 10)

= (3x + 20) = 35 years.

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The ratio of Sara’s age 4 years ago and Vaishali’s age after 4 years is 1: 1. Presently, the ratio of their ages is 5: 3. Find the ratio between Sara’s age 4 years hence and Vaishali’s age 4 years ago.

A.

1 : 3

B.

3: 1

C.

4 : 3

D.

3:4

Answer with explanation

Answer: Option BExplanation

Currently, the ratio of their ages is 5: 3. Suppose, their ages are: 5x and 3x.

Sara’s age 4 years ago = 5x – 4

Vaishali’s age after 4 years = 3x + 4

Ratio of Sara’s age 4 years ago and Vaishali’s age after 4 years is 1 : 1

Therefore,

(5x – 4) / (3x + 4) = 1/1

Solving, we get x = 4

We are required to find the ratio between Sara’s age 4 years hence and Vaishali’s age 4 years ago.

Sara’s age: (5x + 4)

Vaishali’s age: (3x – 4)

Putting the value of x, we get:

(5x + 4) / (3x – 4) = 3/1 = 3:1

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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:

A.

5: 2

B.

7 : 3

C.

9: 2

D.

13: 4

Answer with explanation

Answer: Option BExplanation

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

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

3*x* + 20 = 2*x* + 40

*x* = 20.

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

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What is the age of Teja?

A: Four years ago, Raju was as old as Teja is at present.

B: Sita’s present age is two times of Raju’s present age.

C: The average age of Teja and Sita is 19 years.

A.

Any two statements are sufficient to give answer

B.

Only C is sufficient

C.

All of three statements are necessary to give answer

D.

Even using all the three statements answer cannot be found

Answer with explanation

Answer: Option CExplanation

From the given statements A, B & C

Let the present age of Teja = P

Raju present age = P + 4

Sita’s present age = 2(P + 4)

Average of ages of Sita & Teja = 19

=> (2P + 8 + P)/2 = 19

= 3P + 8 = 38

=> P = 30/3 = 10

Hence, the present age of Teja = P = 10 yrs.

Therefore, by using all the three statements A, B & C we can find the age of Teja.

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The average age of Vishal and Raghavendra is 24 years. If a new person Veerender is also included, the average age is increased by 1.5 years. What is the age of Veerender?

A.

28.5 yrs

B.

29.5 yrs

C.

30.5 yrs

D.

27 yrs

Answer with explanation

Answer: Option AExplanation

According to the given data,

(V + R)/2 = 24

Now, after joining of Veerender,

V + R + D)/3 = 25.5

Hence, Veerender Age = 3(25.5) – 2(24) = 76.5 – 48 = 28.5 years.

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Eighteen years ago, a mother was three times as old as her daughter. Now the mother is only twice as old as her daughter. Then the sum of the present ages of daughter and the mother is ?

A.

84 yrs

B.

96 yrs

C.

116 yrs

D.

108 yrs

Answer with explanation

Answer: Option DExplanation

Let the present ages of the mother and daughter be 2x and x years respectively.

Then, (2x – 18) = 3(x – 18) => x = 36

Required sum = (2x + x) = 108 years.

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The ratio between present ages of Renuka and Sony is 5 : 4 . 4 years ago, Sony’s age was 24 years. What will be Renuka’s age after 5 years ?

A.

25

B.

30

C.

35

D.

40

Answer with explanation

Answer: Option DExplanation

Present age of Sony = 24 + 4 = 28 years

After 5 years Renuka’s age = **7×5 + 5 = 40 years**

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5 years ago Sushma was 5 times as old as her Son. 5 years hence her age will be 8 less than three times the corresponding age of her Son. Find their ages ?

A.

24 and 13 years

B.

48 and 24 years

C.

35 and 11 years

D.

33 and 15 years

Answer with explanation

Answer: Option CExplanation

Let the age of sushma be x and

the age of her son is y

Then five years before x-5=5(y-5) …(1)

Five years hence x+5 = 3(y+5)-8 …..(2)

By soving (1) & (2), we get

5y – 15 = 3y + 7

y = 11 => x = 35

Therefore, the age of Sushma = 35 and her son = 11.

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The average age of a class is 15.8 years. The average age of the boys in the class is 16.4 years and that of the girls is 15.4 years. What is the ratio of boys to girls in the class ?

A.

1:3

B.

2:3

C.

3:2

D.

3:1

Answer with explanation

Answer: Option BExplanation

Let number of boys = x , Let number of girls = y

Total numbers of students = x + y

(x + y) × 15.8 = 16.4x + 15.4y

0.6x = 0.4y

x/y = 0.4/0.6 = 2/3

Ratio of boys and girls in the class is 2:3

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Four person A, B, C and D. The sum of their present age is 176. Four years ago ratio of their age was 11: 9 : 6 : 14, then find who is eldest and youngest among them ?

A.

A is eldest & C is youngest

B.

D is eldest & C is youngest

C.

C is eldest & A is youngest

D.

A is eldest & B is youngest

Answer with explanation

Answer: Option BExplanation

Given sum of present ages of A, B, C & D

A + B + C + D = 176

and also given that,

(A-4) : (B-4) : (C-4) : (D-4) = 11 : 9 : 6 : 14

Let the ratio = x

=> A-4 + B-4 + C-4 + D-4 = 11x + 9x + 6x + 14x

=> (A + B + C + D ) – 16 = 40x

=> 176 – 16 = 40x

=> x = 4

=> A = 44 + 4 = 48

=> B = 40

=> C = 28

=> D = 60

Therefore, from the above conclusions

**D is eldest with 60 years and C is youngest with 28 years of ages.**

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The ratio of present ages of X and Y is 4:5. Which of the following can’t be the ratio of ages of X and Y, 20 years ago ?

A.

2 : 5

B.

8 : 15

C.

9 : 10

D.

3 : 5

Answer with explanation

Answer: Option CExplanation

The ratio of X and Y ages at present is 4:5.

Then, the ratio 20 years ago will not be more than the ratio at present.

So, from the options 9:10 is not satifying => its ratio is 0.9 which is greater than presnt ratio of 0.8.

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Ten years ago, Karan was thrice as old as Shiva was but 10 years hence, he will be only twice as old. Find Shiva’s present age ?

A.

70 years

B.

30 years

C.

60 years

D.

40 years

Answer with explanation

Answer: Option BExplanation

Let Karan’s present age be x years and Shiva’s present age be y years.

Then, according to the first condition,

x – 10 = 3(y – 10) or x – 3y = – 20 ..(1)

Now, Karan’s age after 10 years = (x + 10) years

Shiva’s age after 10 years = (y + 10)

(x + 10) = 2 (y + 10) or x – 2y = 10 ..(2)

Solving (1) and (2), we get x = 70 and y = 30

Karan’s age = 70 years and Shiva’s age = 30 years.

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A man said to his son, “I was two-thirds of your present age when you were born”. IIf the present age of the man is 48 years, find the present age of the son.

A.

25

B.

24

C.

22

D.

28.8

Answer with explanation

Answer: Option DExplanation

Let the Present age of the son be P, which means he was born P years ago.At the time the son was born, the age of the man was : (48 – P). So, according to the statement made by the man, his age when the son was born should be equal to 2/3 of P.

Therefore,

Solving, we get P = 28.8 years; which is the present age of the son.

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Rajeev’s age is four more than the age of Shilpa. The age of Shilpa can be obtained by subtracting four times her age 4 years ago from the four times her age after 4 years. What was Rajeev’s age before 4 years ?

A.

36 years

B.

28 years

C.

32 years

D.

40 years

Answer with explanation

Answer: Option CExplanation

Let Shilpa’s present age is p years

According to question,

p = 4(x+4) – 4(x–4)

p = 4x+16 – 4x+16

p = 32

Shilpa’s present age = 32 years

Rajeev is four years older than Shilpa

=> Shilpa’s present age = Rajeev’s age 4 years before.

=> Rajeev’s age 4 years before = 32 years.

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The ratio of Karthik’s and Kalyan’s ages is 4: 5. If the difference between the present age of Kalyan and the age of Karthik 5 years hence is 3 years, then what is the total of present ages of Karthik and Kalyan?

A.

56 years

B.

62 years

C.

69 years

D.

72 years

Answer with explanation

Answer: Option DExplanation

Let us consider Karthik as K1 and Kalyan as K2.

Given k18+k1k18+k1 and K2 – (K1 + 5) = 3

K2 – K1 = 8

K2 = 8 + K1

Now,

k18+k1= 45k18+k1= 45

=> K1 = 32 years

Therefore K2 = 40 years.

K1 + K2 = 72 years.

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The average of the ages of Sumit, Krishna and Rishabh is 43 years and the average of the ages of Sumit, Rishabh and Rohit is 49 years. If Rohit is 54 years old, what is Krishna’a age ?

A.

48 yrs

B.

42 yrs

C.

40 yrs

D.

36 yrs

Answer with explanation

Answer: Option DExplanation

Let present ages of Sumit=w, Krishna=x, Rishabh=y and Rohit=z , then

w+x+y = 43×3 = 129 —(i) and

w+y+z = 49×3 = 147 —(ii)

Subtracting (i) from (ii), (w+y+z) – (w+x+y)=147 -129 , z- x =18 —(iii)

Given Rohit’s age => z = 54, so from (iii), x = 54-18 = 36

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A.

5

B.

10

C.

15

D.

8

Answer with explanation

Answer: Option BExplanation

Raj Tarun’s age = 0 when he was born.

Then, given his brother is 6 years old.

Then his father is 6 + 32 = 38 when Raj Tarun was born

And his mother is 3 years yonger than his father => so his mother was 35 years old when Raj Tarun was born

and his sister is 25 year younger than his mother

so Raj Tarun’s sister was 10 years old when Raj Tarun was born.

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Today is Varun’s birthday. One year, from today he will be twice as old as he was 12 years ago. How old is Varun today ?

A.

25 years

B.

24 years

C.

23 years

D.

22 years

Answer with explanation

Answer: Option AExplanation

Let varun’s age = x yrs.

From the given conditions,

x+1 = 2(x-12)

x = 25 years.

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At present, the ratio between the ages of Arun and Harish is 4:3. After 6 years, Arun’s age will be 26 years. What is the age of Harish at present ?

A.

15 years

B.

16 years

C.

18 years

D.

21 years

Answer with explanation

Answer: Option AExplanation

Let the present ages of Arun and Harish be 4x and 3x years respectively.

Then, 4x + 6 = 26 => x = 5

Harish’s age = 3x = 15 years.

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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 ?

A.

36 yrs

B.

38 yrs

C.

40 yrs

D.

42 yrs

Answer with explanation

Answer: Option CExplanation

Let the mother’s present age be x years.

Then, the person’s present age = 2/5 x years.

(2x/5 + 8) = 1/2 (x + 8)

2(2x + 40) = 5(x + 8) => x = 40.

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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

A.

15

B.

25

C.

35

D.

45

Answer with explanation

Answer: Option CExplanation

Let A’s age 10 years ago = x years.

Then, B’s age 10 years ago = 2x years.

(x + 10) / (2x+ l0) = 3/4

=> x = 5.

So, the total of their present ages =(x + 10 + 2x + 10)

= (3x + 20) = 35 years.

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A.

19 years

B.

16 years

C.

18 years

D.

20 years

Answer with explanation

Answer: Option DExplanation

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