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Problems on ages

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Problems on ages

  1. 1. Problems on Ages Standard Level VEERARAGAVAN C S APTITUDE TRAINER 98948 34264
  2. 2. What is the Age of Randheer? If 6 years are subtracted from the present age of Randheer and the remainder is divided by 18 then the present age of his grandson Anup is obtained. If Anup is 2 years younger to Mahesh whose age 5 years, then what's the age of Randheer ? a)96 years b)84 years c)48 years d)60 years Anup's age = (5 - 2) years = 3 years Let Randheer's age be x years. Then, (x - 6)/18 = 3 Solving x = 60 1
  3. 3. The difference of their ages ? A says to B "I am twice as old as you were when I was as old as you are." The sum of their ages is 63 years. Find the difference of their ages ? a)27 years b)12 years c)9 years d)6 years 2
  4. 4. Present age of the father? • The ratio of the present ages of a son and his father is 1 : 5 and that of his mother and father is 4 : 5. • After 2 years the ratio of the age of the son to that of his mother becomes 3 : 10. • What is the present age of the father ? • a)30 years b)28 years c)27 years d)None of these • S F = 1 5 ⇒ F = 5 S .....(i) • M F = 4 5 ⇒ M = 4 5 F ....(ii) • ∵ S+2 M+2 = 3 10 • ⇒ 10S + 20 = 3M + 6 ....(iii) 3
  5. 5. what is the age of P ? 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 ? A)15 years B)19 years C)17 years D)12 years 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. 4
  6. 6. What is the present age of Pradhan's father ? 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 ? A)40 years b)50 yearsc)56 years d)Data is inadequate 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. 5
  7. 7. The present age of Shyam ? Four years ago, shyam's age was 3 4 times of that of Ram. Four year hence, Shyam's age will be 5 6 times that of Ram. What is the present age of Shyam ? A)15 yr B)20 yr C)16 yr D)24 yr 4 yr ago, let Ram's age = k yr and Shyam's age = 3K 4 yr Now, Ram's present age = (k + 4) yr and Shyam's present age = ( 3K 4 + 4) yr According to the question, 5 6(k + 4 + 4) = ( 3K 4 + 4 + 4) ⇒ 4 (5k + 40) = 6(3k + 32) 2K = 192 – 160 K = 32 SHYAM’s Age 3K 4 = 24 yr 6
  8. 8. when his brother was born ? Ravi's brother is 3 yr elder to him. His father was 28 yr of age when his sister was born, while his mother was 26 yr of age when he was born. If his sister was 4 yr of age when his brother was born, the ages of Ravi's father and mother respectively when his brother was born ? a)32 yr and 23 yr b)32 yr and 29 yr c)35 yr and 29 yr d)35 yr and 33 yr When Ravi was born, his mother's age was 26 yr and his elder brother was 3 yr elder to him. ∴ Mother's age when brother was born = 26 - 3 = 23 yr Ravi's father was 28 yr of age when his sister was born and his sister was 4 yr of age when his brother was born ∴ Age of father when brother was born = 28 + 4 = 32 yr 7
  9. 9. The son's age after 6 yr ? The average age of a man and his son is 27 yr. The ratio of their ages is 8 : 1, respectively. What will be the son's age after 6 yr ? A)6 yr B)14 yr C)12 yr D)8 yr Let ages of man and his son are 8k yr and k yr, respectively . (8k + k)/2 = 27 9k = 54 k = 6 Age of son after 6 years = 12 yr. 8
  10. 10. How many years? The ages of Harsh and Sumit are 40 yr and 60 yr, respectively. How many year before the ratio of their ages was 3 : 5 ? a)15 yr b)20 yr c)37 yr d)10 yr Let k yr before, the ratio of their ages was 3 : 5. 40 − k 60 − k = 3 5 5(40 – k) = 3 (60 – k ) 20 = 2k K = 10 years. 9
  11. 11. The teacher's age is ? The average age of 9 students and their teacher is 16 yr. The average age of the first four students is 19 yr and that of the last five is 10 yr. The teacher's age is ? a)36 yr b)34 yr c)30 yr d)28 yr Total age of 9 students and a teacher = 10 x 16 = 160 yr Total age of first 4 students = 4 x 19 = 76 yr and total age of last 5 students = 5 x 10 = 50 yr Age of the Teacher = 160 – 126 = 34 yr 10

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