Problem Based on ages
 A is older by 4 years to B at one stage. After 16 years of this stage, A will be thrice his present age and B will be five times his present age. How old would A and B be two years before the initially indicated stage?

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Suppose the ages of A and B are P and Q years respectively.
According to question
Age of A = Age of B + 4 years
⇒ P = Q + 4
After 16 years , Age of A + 16 = 3 x Age of A
⇒ P + 16 = 3P
and Age of B + 16 = 5 x Age of B
⇒ Q + 16 = 5Q
⇒ P = 8 and Q = 4Correct Option: C
Suppose the ages of A and B are P and Q years respectively.
According to question
Age of A = Age of B + 4 years
⇒ P = Q + 4
After 16 years , Age of A + 16 = 3 x Age of A
⇒ P + 16 = 3P
and Age of B + 16 = 5 x Age of B
⇒ Q + 16 = 5Q
⇒ P = 8 and Q = 4
2 years ago their ages
Age of A = 8 – 2 = 6 years
Age of B = 4 – 2 = 2 years
 A is 16 years older than B. But half the age of B is equal to 1/3 of A’s age. Find their present age.

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Suppose the age of A is P years and that of B is Q years.
According to question,
age of A = age of B + 16 years
P = Q + 16
⇒ P – Q = 16 ......(i)Again, age of A = age of B 3 2 ⇒ P = Q 3 2 Correct Option: B
Suppose the age of A is P years and that of B is Q years.
According to question,
age of A = age of B + 16 years
P = Q + 16
⇒ P – Q = 16 ......(i)Again, age of A = age of B 3 2 ⇒ P = Q 3 2
⇒ 2P = 3Q
⇒ 2P – 3Q = 0 ......(ii)
From equations (i) and (ii) , we get
P = 48 years
∴ Q = 48 – 16 = 32 years
Thus, age of A = 48 years and age of B = 32 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 .
 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