Problem on Age MCQ Quiz - Objective Question with Answer for Problem on Age - Download Free PDF

Given:

Ratio of A : B = 5 : 2

Present age of B = 18 years

Formula used:

If A : B = 5 : 2 and B = 18, then A = (5/2) × 18

Calculation:

⇒ A = (5 × 18) ÷ 2

⇒ A = 90 ÷ 2 = 45

∴ The present age of A is: 45 years

Given:

When we reverse the digits of age of the father, we will get the age of son.

One year ago the age of the father was twice that of the son's age.

Concept:

A number ab can be written as (10a + b)

Calculation:

Let father's age = xy i.e. (10x + y)

Therefore, sons age = yx i.e. (10y + x) 

Now, according to the question

⇒ (10x + y) - 1 = 2{(10y + x) - 1}

⇒ 10x + y - 1 = 20y + 2x - 2

⇒ 10x - 2x = 20y - y - 2 + 1

⇒ 8x = 19y - 1

⇒ x = \(\frac{(19y-1)}{{8}}\)

Now, let y = 3 and x = 7

For any other y value, x value combined with y value doesn't give a

realistic age.

So, the current age of father = (10x + y) = (10 × 7 + 3) = 73 years

And, Son's age = (10y + x) = (10 × 3 + 7) = 37 years

∴ The current ages of the father and son are 73 and 37.

Given:

Ratio of ages of A and B, 15 years ago = 4: 5

Ratio of ages of A and B, 5 years hence = 13: 15

Concept:

Difference between ages of two people remains same.

Calculation:

15 years ago difference between age = 5 – 4 = 1 year

5 years hence difference between age = 15 – 13 = 2 year

∵ Difference between ages of two people remains same

New ratio of ages of A and B, 15 years ago = (4: 5) × 2 = 8: 10

And, ratio of ages of A and B, 5 years hence = 13: 15

15 years ago and 5 years hence, total age gap = 15 + 5 = 20

Similarly, age gap between ratio = 13 – 8 = 5 years or 15 – 10 = 5 years

5 years = 20

1 years = 4

Ratio of ages of A and B, 15 years ago = (8: 10) × 4 = 32 : 40

Present ages will be = (32 + 15) : (40 + 15) = 47 : 55

Ratio between sum and difference of their present ages = 102 : 8 = 51 :  4

∴ the correct answer is 51 : 4.

Alternate Method 

15 years ago the ratio of A & B is = 4 : 5

5 year hence the ratio of A & B is = 13 : 15

We see that A & B both have an equal interval of 20 years but their

ratio interval is different i.e for A: (13 - 4) = 9, for B: (15 - 5) = 10,

Now, we have to do equal the ratio intervals,

Now, 5 unit → 20 years

So, 13 unit → \(\frac{20}{5}\times 13 = 52 \) [ which is the age of A, 5 years hence ]

So, 15 unit → \(\frac{20}{5}\times 15 = 60\) [ which is the age of A, 5 years hence ]

Present age of A & B is 47 & 55 respectively

So, the ratio between sum and difference of their present ages,

⇒ ( 55 + 47 ) : ( 55 - 47 )

⇒ 102 : 8

⇒ 51 : 4

Given:

4 years ago, the age of Garvit was three times that of Yuvansh, but one year ago the age of Garvit was two times that of Yuvansh.

Method used:

Elimination method of linear equation in two variable

Calculation:

Let the present age of Garvit be x years and the present age of Yuvansh be y years.

Then, 4 years ago, x - 4 = 3 × (y - 4)...(1)

And one year ago, x - 1 = 2 × (y - 1) ...(2)

Subtracting (2) from (1),

- 3 = y - 10

y = 7 

Substituting y = 7 in (1),

x = 3 × (7 - 4) + 4 = 13   

∴ The difference between the ages of Garvit and Yuvansh is 13 - 7 = 6 years.

Given:

The ratio of the present ages of X and Y is 4 ∶ 5.

After 6 years, the ratio of their ages will be 6 ∶ 7.

Formula Used:

Let the present ages of X and Y be 4k and 5k respectively.

After 6 years, the ages of X and Y will be (4k + 6) and (5k + 6) respectively.

According to the given condition: (4k + 6) / (5k + 6) = 6 / 7

Calculation:

⇒ (4k + 6) / (5k + 6) = 6 / 7

⇒ 7(4k + 6) = 6(5k + 6)

⇒ 28k + 42 = 30k + 36

⇒ 30k - 28k = 42 - 36

⇒ 2k = 6 ⇒ k = 3

The present ages of X and Y are 4k and 5k respectively.

⇒ X = 4k = 4 × 3 = 12 years

⇒ Y = 5k = 5 × 3 = 15 years

The difference between their ages:

⇒ 15 - 12 = 3 years

The correct answer is option 1, 3 years.

Let the ages of the man and his wife be 5x and 8x respectively.

After ten years,

ratio of the man and his wife will be 2 : 3;

⇒ (5x + 10) / (8x + 10) = 2 : 3

Hence, x = 10

The ages of the man and his wife are 50 and 80 respectively.

Given:

Four years ago age ratio of Ram and Rahul = 3 : 4

Present age ratio of Ram and Rahul = 17 : 22

Calculation:

Four years ago age ratio of Ram and Rahul = 3x : 4x

According to the question

(3x + 4)/(4x + 4) = 17/22

⇒ 22 × (3x + 4) = 17 × (4x + 4)

⇒ 66x + 88 = 68x + 68

⇒ 68x – 66x = 88 – 68

⇒ 2x = 20

⇒ x = 10

Present age of Ram = 3 × 10 = 30 + 4 = 34

Present age of Sunil = 34 – 5 = 29 years 

∴ the correct answer is 29 years.

Shortcut Trick 

Many students ignore to read full question, So please read full question before solving it. 
In the last line of question there is mentioned that Ram is 5 years older than Sunil. 
So if you Calculate Ram's age than you also can calculate Sunil's age.

Given:

Karan was born 3 years after his parent's marriage.

His father is 6 years older than his mother but 26 years older than Karan.

Karan is 12 years of age as on today.

Calculation:

According to question,

⇒ F = 6 + M

⇒ F = 26 + K 

Since now karan is 12 years old so,

⇒ K = 12,

⇒ F = 38,

⇒ M = 32

Now at the time of birth age will be ,

⇒ F = 26

⇒ M = 20 

Since karan was born 3 years after his parents marriage so

Age of motrher = 20 - 3 = 17

∴ 'The correct answer is 17 years.

Given:

Manish age = 20 years

Greece age = 20/5 = 4 years

Let after x years Manish will become three times as old as Greece:

(20 + x) = 3 × (4 + x)

20 + x = 12 + 3x

2x = 8

x = 4

After 4 years Manish's age will be 24 years and Greece's age 8 years.

When Manish's age is 24 years old he became three times as old as Greece.

Hence, the correct answer is "24".

Given:

Amita's father was 38 years old when she was born.

Her mother was 36 years old when her brother was born.

Her brother was four years younger than her.

Calculation:

Let the present age of Amita be P years.

So,

The age of her father = (38 + P) years

The age of her brother = (P - 4) years

The age of her mother = 36 + (P - 4) = (32 + P) years

Now, the age difference between her parents = (38 + P) - (32 + P) = 6 years

∴ The difference between the ages of her parents is 6 years.

Given:

(Man's age + 15 years) = 4(Man's age - 15 years)

Calculation:

Let the present age of the man be x years

According to the question,

⇒ (x + 15) = 4(x - 15)

⇒ x + 15 = 4x - 60

⇒ 4x - x = 15 + 60

⇒ 3x = 75

⇒ x = 25

∴ The present age of man is 25 years.

Let the ages of Keshav and Danish after six years be 19x and 17x respectively

⇒ Present age of Keshav = (19x - 6) years

⇒ Present age of Danish = (17x - 6) years

According to question, age of Keshav 4 years ago is equal to present age of Danish

19x - 6 - 4 = 17x - 6

⇒ 2x = 4

⇒ x = 2

Present age of Keshav = (19 × 2) - 6 = 32 years

Present age of Danish = (17 × 2) - 6 = 28 years

Sum of their ages = 32 + 28 = 60

∴ The sum of their ages is 60.

Given:

Wife was born 23 years ago (which means her present age is 23 years

Ratio of ages of Rahul and his wife 7 years from now will be 7 : 6

Calculation:

Let the present age of husband be x years.

Age of husband 7 years hence = x + 7

Present age of wife = 23 years

Age of wife after 7 years = 30 years

According to the question,

Ratio of ages of husband and wife 7 years from now = 7 : 6

⇒ (x + 7)/30 = 7/6

⇒ x + 7 = 35

⇒ x = 28 years

Given,

Let present age of Radha and Ram be a years and b years respectively.

⇒ (a - 6) : (b - 6) = 5 : 8

⇒ 8a - 48 = 5b - 30

⇒ 8a - 5b = 18

Then,

⇒ b - a = 6

Solving,

a = 16 years and b = 22 years

Then,

⇒ (16 + ?) : (22 + ?) = 13 : 16

⇒ 256 + 16? = 286 + 13?

⇒ ? = 10

∴ after 10 years ratio will become 13 :16.

Given:

Ratio between the present ages of Ram and Ramesh is 3 : 5

After 7 years the ratio of their ages will be 4 : 5.

Calculation:

Let the present age of Ram and Ramesh be 3x and 5x

According to the question,

\(\frac{3x +7}{5x + 7} = \frac{4}{5}\)

⇒ 15x + 35 = 20x + 28

⇒ 35 - 28 = 20x - 15x

⇒ 5x = 7

⇒ x = 7/5

So, the present age of Ramesh = 5 × 7/5

⇒ 7 years

∴The present age of Ramesh is 7 years.