Problem Based on ages
 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?

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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
 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?

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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 yearsThe 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 yearsThe 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.
 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?

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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
 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?

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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 = 58Correct 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 .
 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 ______.

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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 yearsCorrect 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