## Problem Based on ages

#### Problem Based on ages

1. Mrs. Lata was 3 times as old as her son 8 years ago. Their total age is 64 years now. How old (in years) is Mrs. Lata now?

1. Suppose present age of Mrs. Lata = P years
Present age of son = Q years
∴ Their total age = 64 years
P + Q = 64 ....... (i)
According to question,
8 years ago , present age of Mrs. Lata - 8 years = 3 × ( present age of her son - 8 years )
⇒ P – 8 = 3 (Q – 8)
⇒ P – 8 = 3Q – 24
⇒ P – 3Q = – 16 ......(ii)

##### Correct Option: D

Suppose present age of Mrs. Lata = P years
Present age of son = Q years
∴ Their total age = 64 years
P + Q = 64 ....... (i)
According to question,
8 years ago , present age of Mrs. Lata - 8 years = 3 × ( present age of her son - 8 years )
⇒ P – 8 = 3 (Q – 8)
⇒ P – 8 = 3Q – 24
⇒ P – 3Q = – 16 ......(ii)
From equations (i) and (ii), we get
4Q = 80 ⇒ Q = 20
Putting the value of Q in eq.(i)
∴ Age of Mrs. Lata = 64 – 20 = 44 years

1. Hema was twice as old as Geeta 10 years ago. How old is Geeta today, if Hema will be 40 years old 10 years henceforth?

1. 10 years after , The age of Hema = 40 years
The present age of Hema = 40 – 10 = 30 years
The age of Hema 10 years ago = The present age of Hema - 10 years = 30 – 10 = 20 years

 The age of Geeta 10 years ago = 20 = 10 years 2

##### Correct Option: B

10 years after , The age of Hema = 40 years
The present age of Hema = 40 – 10 = 30 years
The age of Hema 10 years ago = The present age of Hema - 10 years = 30 – 10 = 20 years

 The age of Geeta 10 years ago = 20 = 10 years 2

So, the present age of Geeta = The age of Geeta 10 years ago + 10 years = 10 + 10 = 20 years.

1. Jais and his father has an age difference of 35 years now. After 5 years, the sum of their age is 125. What will be the age of Jais and his father after 12 years from now?

1. Suppose the age of Jais = P years
The age of his father - The age of Jais = 35 years
Therefore, his father’s age = P + 35 years
According to question ,
After 5 years,the sum of their age is 125.
⇒ (P + 5) + (P + 35 + 5) = 135
⇒ 2P + 45 = 135
⇒ 2P = 135 – 45

 ∴ P = 90 = 45 2

##### Correct Option: B

Suppose the age of Jais = P years
The age of his father - The age of Jais = 35 years
Therefore, his father’s age = P + 35 years
According to question ,
After 5 years,the sum of their age is 125.
⇒ (P + 5) + (P + 35 + 5) = 135
⇒ 2P + 45 = 135
⇒ 2P = 135 – 45

 ∴ P = 90 = 45 2

Age of Jais after 12 years = P + 12 = 40 + 12 = 52 years
Age of his father after 12 years = 40 + 35 + 12 = 87 years

1. The average age of the present ages of Amit and Anil is 32 years. If Amit is 6 years older than Anil, what is Anil’s present age?

1. The average age of the present ages of Amit and Anil = 32 years
Total age of Amit and Anil = 2 × 32 = 64 years
Suppose, age of Anil = P years
∴ Age of Amit = P + 6 years
According to the question, P + P + 6 = 64
⇒ 2P = 64 – 6 = 58

##### Correct Option: D

The average age of the present ages of Amit and Anil = 32 years
Total age of Amit and Anil = 2 × 32 = 64 years
Suppose, age of Anil = P years
∴ Age of Amit = P + 6 years
According to the question, P + P + 6 = 64
⇒ 2P = 64 – 6 = 58

 ∴ P = 58 = 29 years 2

Hence , Anil’s present age is 29 years .

1. A man was 32 years of age when he had his first son. His wife was 35 years of age when his son attained the age of 7 years. The difference between the age of the father and the mother is ______.

1. The age of father when his son attained the age of 7 years = 32 + 7 = 39 years
The age of mother when her son attained the age of 7 years = 35 years
∴ Required difference = The age of father when his son attained the age of 7 years - The age of mother when her son attained the age of 7 years

##### Correct Option: D

The age of father when his son attained the age of 7 years = 32 + 7 = 39 years
∴ Required difference = The age of father when his son attained the age of 7 years - The age of mother when her son attained the age of 7 years
The difference between the ages of father and mother = (39 – 35) years = 4 years