Problem Based on ages
 Your mother is 4 years younger than your father who is 6 times older than you. If your age is 6 years, what is your mother’s age?

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Given : The age of person is 6 years
His father’s age = 6 × 6 = 36 yearsCorrect Option: D
Given : The age of person is 6 years
His father’s age = 6 × 6 = 36 years
Therefore, the age of his mother = His father’s age  4 years = 36 – 4 = 32 years
 The total age of a mother and her daughter is 60 years. The difference between their ages is 30 years. Find out the age of the mother.

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Suppose, daughter’s age is P years.
Therefore, mother’s age will be ( P + 30 ) years.
The total age of a mother and her daughter = 60 years.
⇒ P + ( P + 30 ) = 60
⇒ 2P = 60 – 30Correct Option: B
Suppose, daughter’s age is P years.
Therefore, mother’s age will be ( P + 30 ) years.
The total age of a mother and her daughter = 60 years.
⇒ P + ( P + 30 ) = 60
⇒ 2P = 60 – 30∴ P = 30 = 15 2
Therefore , the age of the mother is 15 years .
 ‘X’ and her grandfather differ in their ages by 50 years. After 6 years, if the sum of their ages is 152, their present ages are

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Suppose the present age of X = P years
Her grandfather’s present age = P + 50 years
According to question P + 6 + P + 50 + 6
⇒ 2P + 62 = 152
⇒ 2P = 152 – 60Correct Option: C
Suppose the present age of X = P years
Her grandfather’s present age = P + 50 years
According to question P + 6 + P + 50 + 6
⇒ 2P + 62 = 152
⇒ 2P = 152 – 60∴ present age of 'X' = P = 90 = 45 Years 2
and present age of grand father = P + 50 = 45 +50 = 95 years
 Today is Ketan’s birthday. One year from today he will be twice as old as he was 10 years ago. How old is Ketan today?

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Suppose the present age of Ketan is P years.
According to question,
present age of Ketan + 1 year = 2 ( present age of Ketan  10 years )
P + 1 = 2 (P – 10)
⇒ P + 1 = 2P – 20
⇒ 2P – P = 20 + 1Correct Option: C
Suppose the present age of Ketan is P years.
According to question,
present age of Ketan + 1 year = 2 ( present age of Ketan  10 years )
P + 1 = 2 (P – 10)
⇒ P + 1 = 2P – 20
⇒ 2P – P = 20 + 1
∴ P = 21 years
Therefore ,present age of Ketan is 21 years .
 A father’s age is now three times that of his elder daughter. 5 years back, his age was 8 times that of his younger daughter. If the difference of ages of the two daughters is 5 years, what is the age of the father now?

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Suppose the present age of younger daughter is P years.
Given :  Present age of the elder daughter  the present age of younger daughter = 5
∴ Present age of the elder daughter = P + 5 years
Present age of the father = 3 × Present age of the elder daughter
Present age of the father = 3(P + 5) years.
According to the question,
5 years before, 8 × ( the present age of younger daughter  5 years ) = Present age of the father  5 years
⇒ 8 (P – 5) = (3P + 15) – 5Correct Option: D
Suppose the present age of younger daughter is P years.
Given :  Present age of the elder daughter  the present age of younger daughter = 5
∴ Present age of the elder daughter = P + 5 years
Present age of the father = 3 × Present age of the elder daughter
Present age of the father = 3(P + 5) years.
According to the question,
5 years before, 8 × ( the present age of younger daughter  5 years ) = Present age of the father  5 years
⇒ 8 (P – 5) = (3P + 15) – 5
⇒ 8P – 40 = 3P + 10
⇒ 8P – 3P = 10 + 40∴ P = 50 = 10 years 5
Present age of father = 3(P + 5) = 3 × 10 + 15 = 45 years { ∴ putting , P = 10 }