Problem Based on ages
- Neela is now 3 times as old as her daughter Leela. Ten years back, Neela was 5 times as old as Leela. The age of Leela is
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Suppose the present age of Leela is P years.
Therefore, the present age of Neela = 3P years
10 years ago ,5 × ( the present age of Leela - 10 years ) = ( the present age of Neela - 10 years )
5 (P – 10) = (3P – 10)Correct Option: D
Suppose the present age of Leela is P years.
Therefore, the present age of Neela = 3P years
10 years ago ,5 × ( the present age of Leela - 10 years ) = ( the present age of Neela - 10 years )
5 (P – 10) = (3P – 10)
⇒ 5P – 50 = 3P – 10
⇒ 5P – 3P = 50 – 10
⇒ 2P = 40∴ P = 40 = 20 years 2
Therefore , the present age of Leela is 20 years.
- 2 years ago a mother was 4 times as old as her son. 6 years from now her age will become more than double her son’s age by 10 years. What is the present ratio of their ages?
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Suppose the present age of son = P years
Present age of mother = Q years
According to question,
4 (P – 2) = Q – 2
⇒ 4P – 8 = Q – 2
⇒ 4P – Q = 6 ...(i)
2 (P + 6) + 10 = Q + 6
⇒ 2P + 12 + 10 = Q + 6Correct Option: B
Suppose the present age of son = P years
Present age of mother = Q years
According to question,
4 (P – 2) = Q – 2
⇒ 4P – 8 = Q – 2
⇒ 4P – Q = 6 ...(i)
2 (P + 6) + 10 = Q + 6
⇒ 2P + 12 + 10 = Q + 6
⇒ 2P – Q = –16 ...(ii)
From equations (i) and (ii)
P = 11
∴ Q = 4 × 11 – 6 = 38
Required the present ratio of their ages = 38 : 11
- Mother was three times the age of her daughter 5 years ago. After 5 years, mother will be twice as old as her daughter. How old is the daughter today?
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Suppose the present age of daughter = P years
and, the present age of mother = Q years
According to questions,
5 years ago , 3 × ( the present age of daughter - 5 ) = ( the present age of mother - 5 )
3 (P – 5) = (Q – 5)
⇒ 3P – 15 = Q – 5
⇒ 3P – Q = 10 .......(i)
After five years , 2 × ( the present age of daughter + 5 ) = ( the present age of mother + 5 )
2 (P + 5) = Q + 5
⇒ 2P + 10 = Q + 5Correct Option: C
Suppose the present age of daughter = P years
and, the present age of mother = Q years
According to questions,
5 years ago , 3 × ( the present age of daughter - 5 ) = ( the present age of mother - 5 )
3 (P – 5) = (Q – 5)
⇒ 3P – 15 = Q – 5
⇒ 3P – Q = 10 .......(i)
After five years , 2 × ( the present age of daughter + 5 ) = ( the present age of mother + 5 )
2 (P + 5) = Q + 5
⇒ 2P + 10 = Q + 5
⇒ 2P – Q = –5 .......(ii)
From equations (i) and (ii) , we get
3P – 2P = 10 – (–5)
⇒ P = 15 years
Hence, the present age of daughter is 15 years .
- The age of a father is twice that of his son’s at present age. After 5 years the sum of their ages will be 85. How old are they now?
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Suppose the present age of son = P years
Age of father = 2P years
According to question
P + 5 + 2P + 5 = 85
⇒ 3P + 10 = 85
⇒ 3P = 85 – 10 = 75Correct Option: D
Suppose the present age of son = P years
Age of father = 2P years
According to question
P + 5 + 2P + 5 = 85
⇒ 3P + 10 = 85
⇒ 3P = 85 – 10 = 75Present age of son P = 75 = 25 Years 2
and Father's present age = 2P = 50 years
- Amit was born 5 years before Rakesh, Rakesh is 3 years younger to Anil. If Amit is now 17 years old, how old is Anil?
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The present age of Amit = 17 years
5 years before , age of Rakesh = The present age of Amit - 5 years = 17 – 5 = 12 yearsCorrect Option: C
The present age of Amit = 17 years
5 years before , age of Rakesh = The present age of Amit - 5 years = 17 – 5 = 12 years
∴ Age of Anil = age of Rakesh + 3 years = 12 + 3 = 15 years
