Problems on Ages
- The ratio between present age of Kunal and Ganesh is 3 : 5. If 4 years later Kunal will be younger then Ganesh by 12 years. What is the present age of Kunal ?
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Let the present age of Kunal be 3x year and the
present age of Ganesh = 5x years.
According to question ,
(5x + 4 ) - (3x + 4 ) = 12Correct Option: D
Let the present age of Kunal be 3x year and the
present age of Ganesh = 5x years.
According to question ,
(5x + 4 ) - (3x + 4 ) = 12
⇒ 2x = 12
∴ x = 6
∴ Present age of Kunal = 3x = 3 x 6 = 18 year
- If the age of P and R are added to twice the age of Q the total becomes 59. If the ages of Q and R are added to thrice the age of P the total becomes 68. And if the age of P is added to thrice the age of Q and thrice the age of R, the total becomes 108. what is the age of P T?
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P + R + 2 Q = 59, ....(i)
Q + R + 3 P = 68 .....(ii)
and P + 3 (Q + R) = 108 ......(iii)Correct Option: D
P + R + 2 Q = 59, ....(i)
Q + R + 3 P = 68 .....(ii)
and P + 3 (Q + R) = 108 ......(iii)
Solving the above three equations, we get
⇒ P + 3 (68 - 3P) = 108
⇒ P + 204 - 9P = 108
∴ P = 12 years.
- After 6 years Pradhan's age will be 3/7 times the age of his father. 10 years ago the ratio in the age of Pradhan and his father was 1 : 5. What is the present age of Pradhan's father ?
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Let the present age of Pradhan be P years and his father's age = Q years.
From 1st condition,
(P + 6) = (Q + 6 ) x 3/7
⇒ 7P + 42 = 3Q + 18
⇒ 7P - 3Q = -24 ...(i)
From 2nd condition
(P - 10) / (Q - 10) = 1/5
⇒ 5P - 50 = Q - 10
⇒ 5P - Q = 40 .....(ii)Correct Option: B
Let the present age of Pradhan be P years and his father's age = Q years.
From 1st condition,
(P + 6) = (Q + 6 ) x 3/7
⇒ 7P + 42 = 3Q + 18
⇒ 7P - 3Q = -24 ...(i)
From 2nd condition
(P - 10) / (Q - 10) = 1/5
⇒ 5P - 50 = Q - 10
⇒ 5P - Q = 40 .....(ii)
Multiplying equation (ii) by 3 and subtracting from (i) we get
P = 18, Q = 50
So present age of Pradhan's father = 50 years.
- Raman's present age is three times his daughter's and nine-thirteenth of his mother's present age. The sum of the present ages of all three of them is 125 yr. What is the difference between the present ages of Raman's daughter and Raman's mother?
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Let age of Raman's daughter = N yr
Then, age of Raman's = 3N yr
and age of Raman's mother = (13/9) x 3N = 13N/3 yr
According to the question, N + 3N + 13N/3 = 125Correct Option: C
Let age of Raman's daughter = N yr
Then, age of Raman's = 3N yr
and age of Raman's mother = (13/9) x 3N = 13N/3 yr
According to the question, N + 3N + 13N/3 = 125
⇒ 3N + 9N + 13N = 125 x 3
∴ N = (125 x 3)/25 = 15
Hence, required difference = 13N/3 - N = 10N/3
= (10 x 15)/3 = 50 yr
- Two trains of length 512 m and 528 m are running towards each others on parallel lines at 84 km/h and 60 km/h, respectively. In what time, will they be clear of each other from the moments they meet ?
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Relative speed = (84 + 60) km/h = 144 km/h = 144 x (5/18) = 8 m/s
Distance covered in passing each other = 512 + 528 = 1040 mCorrect Option: A
Relative speed = (84 + 60) km/h = 144 km/h = 144 x (5/18) = 8 m/s
Distance covered in passing each other = 512 + 528 = 1040 m
∴ Required time = 1040/40 = 26 s
