**Problems On Ages**

11) Sachin is 40 years old and Vijay is 60 years old. How many decades ago was the proportion of their ages 3 : 5?

A) 37 years

B) 27 years

C) 20 years

D) 10 years

If the ratio was 3 : 5, ‘A’ years ago.

Then, 7A – 6A = 4

A = 4

Then, {( 40 – A)/(60 – A)}= (3/5)

5 (40 – A) = 3(60 – A)

2A = 20

A = 10

D) 10 Years

12) 15 years hence, Karthikh will be just Quadrice as old as he was 15 years ago, How old is Karthikh at now? [ Quadrice = 4 Times ]

A) 35

B) 25

C) 20

D) 30

Let the current age of Karthikh = A years

Then, A+15 = 4(A – 15)

Therefore A = 25

B) 25 Years old

13) The current ages of 3 individuals are in the ratio 4:7:9. 0.8 decades ago, the sum of their ages was 56. Find their current ages in years

A) 16, 28, 36

B) 18, 30, 38

C) 20, 32, 46

D) None of these

Let their current ages are 4A, 7A and 9A years correspondingly.

Then, (4A – 8) + (7A – 8) + (9A – 8) = 56

20A = 80

A = 4

Their current ages are

16 years, 28 years and 36 years correspondingly.

A) 16, 28, 36

14) The proportion between the college days ages of Rathi and Tharan is 5 : 6 correspondingly. If the proposition between the 1/3 age of Rathi and half of Tharan’s age is 5 : 9, then what is the college days age of Tharan?

A) 10 years

B) 25 years

C) 30 years

D) Cannot be determined

E) None of these

Then, Tharan’s age cannot be determined.

D) Can’t be determined

15) 1 Decade ago, Karthikh’s mother was quadrice older than her son. After one decade, the mother will be two times older than her son. The current age of Karthikh is?

[Decade = 10 Years; quadrice= 4 times]

A) 8 years

B) 12 years

C) 20 years

D) 23 years

Let Karthikh’s age 10 years ago be A year

His mother’s age 1 decade ago = 4A

(4A + 10) + 10 = 2 (A + 10 +10)

2A = 20 or A =10

Current age of Karthikh = (A + 10)

= 20 years

C) 20 Years

16) A person’s age is 125% of what it was one decade ago, but 83(1/3)% of what it will be after one decade. What is his current age? [1 decade = 10 years]

A) 35 years

B) 40 years

C) 50 years

D) 55 years

Let, current age is A years.

Then, 125% of (A – 10) = A

and, 83(1/3)% of (A + 10) = A

Therefore 125% of (A-10) = 83(1/3)% of (A+10)

or, (5/4) (A – 10) =(5/6)(A+10)

or, (5/4)A -(5/6)A = (50/6)+(50/4)

or, (5A/12)= (250/12) or,

A=50 years.

C) 50 Years

17) One decade ago, X was half of Y in age. If the proportion of their current ages is 3:4, what will be the overall of their current ages?

A) 10 years

B) 20 years

C) 25 years

D) None of these

Let the ages of X and Y 1 decade ago be A and 2A years correspondingly.

Then, [ (A +10)/2A+10) ] = (3/4)

4 (A – 10) = 3(2A – 10)

2A = 10

A = 5

Therefore,

Sum of theircurrent ages = (A + 10) + (2A + 10) = (3A + 20)

= 35 years.

D) None of these

18) 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

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

B) 10 Years Old

19) A person is 24 years elder than his daughter. In 2 years, person’s age will be 2 times the age of his daughter. Then the current age of the daughter is:

A) 14 years

C) 20 years

B) 18 years

D) 22 years

Let, daughter’s current age is A years. Then, person’s current age = (A +24) years.

(A + 24) + 2 = 2 (A + 2)

A + 26 = 2A + 4

A = 22

D) 22 Years

20) 0.2 decades ago a person was 6 times as old as his daughter, After 18 years, he will be two times as old as his daughter. Then their current ages are,

[0.2 decades = 2 years]

A) 7

B) 9

C) 11

D) None of these

None of these.

D) None of these