Problem Based on ages
- The sum of the ages of father and a son presently is 70 years. After 10 years, the son’s age is exactly half that of the father. What are their ages now?
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Suppose the age of son = P years
∴ Age of the father = 70 – P
According to question ,
After 10 years , 2 ( age of son + 10 years ) = ( Age of the father + 10 years )
After 10 years , 2 (P + 10) = 70 – P + 10
⇒ 2P + 20 = 80 – P
⇒ 2P + P = 80 – 20
⇒ 3P = 60Correct Option: B
Suppose the age of son = P years
∴ Age of the father = 70 – P
According to question ,
After 10 years , 2 ( age of son + 10 years ) = ( Age of the father + 10 years )
After 10 years , 2 (P + 10) = 70 – P + 10
⇒ 2P + 20 = 80 – P
⇒ 2P + P = 80 – 20
⇒ 3P = 60∴ P = 60 = 20 years 3
The age of son = 20 years
Age of Father = 70 - P = 70 - 20 = 50 years
- Ram got married 8 years ago. His present age is 6/5 times his age at the time of marriage. Ram's sister was 10 years younger to him at the time of his marriage. What is the present age of Ram's sister?
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Let the present age of Ram be x years.
Correct Option: B
Let the present age of Ram be x years; then
8 years ago Ram age = x - 8
According to question,
His present age is 6/5 times his age at the time of marriage.
x =( x - 8) 6/5
⇒ 5x = 6x - 48
∴ x = 48
Age of Ram at the time of his marriage = 48 - 8 = 40
According to question,
Ram's sister was 10 years younger to him at the time of his marriage
Hence, Ram's sister age at the time of his marriage = 40 - 10 = 30 years.
So Present age of Ram's Sister = 30 + 8 = 38
- The sum of the ages of a father and his son is 45 years. Five years ago, the product of their ages was four times the father's age at that time. What are their present ages?
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Method 1
Lt us assume the present age of father is P and son age is Q.
According to question,
P + Q = 45
Method 2
Let the present ages of father and his son be x and (45 - x) years respectively.Correct Option: B
Lt us assume the present age of father is P and son age is Q.
According to question,
P + Q = 45.................. (1)
Five years ago, the father age = P - 5
Five years ago, the son age = Q - 5
According to question,
Five years ago, the product of their ages was four times the father's age at that time.
(P - 5) (Q - 5) = 4 (P - 5)
PQ - 5P - 5Q + 25 = 4P - 20
PQ - 5P - 5Q + 25 - 4P + 20 = 0
⇒ PQ - 9P - 5Q + 45 = 0
⇒ P(Q - 9) - 5(Q - 9) = 0
⇒ (Q - 9) (P - 5) = 0
⇒ (Q - 9) = 0 or (P - 5) = 0
⇒ Q = 9 or P = 5
Put the vale of Q in equation (1), we will get.
if Q = 9 then P = 45 - 9 = 36 which is matched our answer.
If P = 5 then Q = 45 - 5 = 40 years which is not match our answer.
Method 2
Let the present ages of father and his son be x and (45 - x) years respectively;
then according to question,
(x - 5) (45 - x - 5) = 4 (45 - x -5)
⇒ x - 5 = 4
⇒ x = 9
Now, Father's age = 45 - x = 45 - 9 = 36 years
- The difference between the present ages of Arun and Barun is 14 years. 7 years ago the ratio of their ages was 5 : 7 respectively. The present age of Barun is :
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Let the present ages of Arun and Barun are x and x + 14 years respectively.
Correct Option: D
Let the present ages of Arun and Barun are x and x +14 years respectively; then
According to question, 7 years ago the ratio of their ages was 5 : 7
(x - 7)/(x + 14 - 7) = 5/7
⇒ (x - 7)7 = 5(x+14 - 7)
⇒ 7x - 49 = 5x + 35
⇒ 2x = 84
∴ x = 42
Hence, age of Barun = 42 + 14 = 56 years
- The ratio between the ages of Ram and Mohan is 4 : 5 and that between Mohan and Anil is 5 : 6. If sum of the ages of three be 90 years, what is the age of Mohan ?
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Here, ratio of ages of Ram, Mohan and Anil = 4 : 5: 6
Let their present ages be 4x, 5x and 6x years respectively.Correct Option: D
Here, ratio of ages of Ram, Mohan and Anil = 4 : 5: 6
Let their present ages be 4x, 5x and 6x years respectively.
then 4x + 5x + 6x = 90
⇒ 15x = 90
∴ x = 6
Hence, age of Mohan = 5 x 6 = 30 years
