TEST - 6
1. The sum of ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child? (a) 4 YEARS (b) 8 YEARS (c) 10 YEARS (d) NONE OF THESE EXPLANATION: Let the ages of children be x, (x + 3), (x + 6), (x + 9) and (x + 12) years. Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50 5x = 20 => x = 4. Age of the youngest child = x = 4 years. |
1. The sum of ages of 5 children born at the intervals of 3 years each is 50 years. What is the age of the youngest child? (a) 4 YEARS (b) 8 YEARS (c) 10 YEARS (d) NONE OF THESE EXPLANATION: Let the ages of children be x, (x + 3), (x + 6), (x + 9) and (x + 12) years. Then, x + (x + 3) + (x + 6) + (x + 9) + (x + 12) = 50 5x = 20 => x = 4. Age of the youngest child = x = 4 years. |
2. A father said to his son, “I was as old as you are at the present at the time of your birth”. If the father’s age is 38 years now, the son’s age five years back was: (a) 14 YEARS (b) 19 YEARS (c) 33 YEARS (d) 38 YEARS EXPLANATION: Let the son’s present age be x years. Then, (38 – x) = x 2x = 38 => x = 19. Son’s age 5 years back (19 – 5) = 14 years. |
2. A father said to his son, “I was as old as you are at the present at the time of your birth”. If the father’s age is 38 years now, the son’s age five years back was: (a) 14 YEARS (b) 19 YEARS (c) 33 YEARS (d) 38 YEARS EXPLANATION: Let the son’s present age be x years. Then, (38 – x) = x 2x = 38 => x = 19. Son’s age 5 years back (19 – 5) = 14 years. |
3. A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 27, then how old is B? (a) 7 (b) 8 (c) 9 (d) 10 EXPLANATION: Let C’s age be x years. Then, B’s age = 2x years. A’s age = (2x + 2) years. (2x + 2) + 2x + x = 27 5x = 25 => x = 5. Hence, B’s age = 2x = 10 years. |
3. A is two years older than B who is twice as old as C. If the total of the ages of A, B and C be 27, then how old is B? (a) 7 (b) 8 (c) 9 (d) 10 EXPLANATION: Let C’s age be x years. Then, B’s age = 2x years. A’s age = (2x + 2) years. (2x + 2) + 2x + x = 27 5x = 25 => x = 5. Hence, B’s age = 2x = 10 years. |
4. Present ages of Sameer and Addan are in the ratio of 5:4 respectively. Three years hence, the ratio of their ages will become 11:9 respectively. What is Addan’s present age in years? (a) 24 (b) 27 (c) 40 (d) NONE OF THESE EXPLANATION: Let the present ages of Sameer and Addan be 5x years and 4x years respectively. Then, 5x + 3 = 11 4x + 3 9 9(5x + 3) = 11(4x + 3) 45x + 27 = 44x + 33 45x – 44x = 33 – 27 => x = 6. Addan’s present age = 4x = 24 years. |
4. Present ages of Sameer and Addan are in the ratio of 5:4 respectively. Three years hence, the ratio of their ages will become 11:9 respectively. What is Addan’s present age in years? (a) 24 (b) 27 (c) 40 (d) NONE OF THESE EXPLANATION: Let the present ages of Sameer and Addan be 5x years and 4x years respectively. Then, 5x + 3 = 11 4x + 3 9 9(5x + 3) = 11(4x + 3) 45x + 27 = 44x + 33 45x – 44x = 33 – 27 => x = 6. Addan’s present age = 4x = 24 years. |
5. A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is: (a) 14 YEARS (b) 18 YEARS (c) 20 YEARS (d) 22 YEARS EXPLANATION: Let the son’s present age be x years. Then, man’s present age = (x + 24) years. (x + 24) + 2 = 2(x + 2) x + 26 = 2x + 4 => x = 22. |
5. A man is 24 years older than his son. In two years, his age will be twice the age of his son. The present age of his son is: (a) 14 YEARS (b) 18 YEARS (c) 20 YEARS (d) 22 YEARS EXPLANATION: Let the son’s present age be x years. Then, man’s present age = (x + 24) years. (x + 24) + 2 = 2(x + 2) x + 26 = 2x + 4 => x = 22. |
6. Six years ago, the ratio of the ages of Kanwal and Saira was 6:5. Four years hence, the ratio of their ages will be 11:10. What is Saira’s age at present? (a) 16 YEARS (b) 18 YEARS (c) 20 YEARS (d) NONE OF THESE EXPLANATION: Let the ages of Kanwal and Saira 6 years ago be 6x and 5x years respectively. Then, (6x + 6) + 4 = 11 (5x + 6) + 4 10 10(6x + 10) = 11(5x + 10) 5x = 10 => x = 2. Saira’s present age = (5x + 6) = 16 years. |
6. Six years ago, the ratio of the ages of Kanwal and Saira was 6:5. Four years hence, the ratio of their ages will be 11:10. What is Saira’s age at present? (a) 16 YEARS (b) 18 YEARS (c) 20 YEARS (d) NONE OF THESE EXPLANATION: Let the ages of Kanwal and Saira 6 years ago be 6x and 5x years respectively. Then, (6x + 6) + 4 = 11 (5x + 6) + 4 10 10(6x + 10) = 11(5x + 10) 5x = 10 => x = 2. Saira’s present age = (5x + 6) = 16 years. |
7. The sum of the present ages of a father and his son is 60 years. Six years ago, father’s age was five times the age of the son. After 6 years, son’s age will be: (a) 12 YEARS (b) 14 YEARS (c) 18 YEARS (d) 20 YEARS EXPLANATION: Let the present ages of son and father be x and (60 -x) years respectively. Then, (60 – x) – 6 = 5(x – 6) 54 – x = 5x – 30 6x = 84 => x = 14. Son’s age after 6 years = (x+ 6) = 20 years. |
7. The sum of the present ages of a father and his son is 60 years. Six years ago, father’s age was five times the age of the son. After 6 years, son’s age will be: (a) 12 YEARS (b) 14 YEARS (c) 18 YEARS (d) 20 YEARS EXPLANATION: Let the present ages of son and father be x and (60 -x) years respectively. Then, (60 – x) – 6 = 5(x – 6) 54 – x = 5x – 30 6x = 84 => x = 14. Son’s age after 6 years = (x+ 6) = 20 years. |
8. At present, the ratio between the ages of Amir and Dua is 4:3. After 6 years, Amir’s age will be 26 years. What is the age of Dua at present? (a) 12 YEARS (b) 15 YEARS (c) 19 & HALF (d) 21 YEARS EXPLANATION: Let the present ages of AMIR and DUA be 4x years and 3x years respectively. Then, 4x + 6 = 26 4x = 20 x = 5. DUA’s age = 3x = 15 years. |
8. At present, the ratio between the ages of Amir and Dua is 4:3. After 6 years, Amir’s age will be 26 years. What is the age of Dua at present? (a) 12 YEARS (b) 15 YEARS (c) 19 & HALF (d) 21 YEARS EXPLANATION: Let the present ages of AMIR and DUA be 4x years and 3x years respectively. Then, 4x + 6 = 26 4x = 20 x = 5. DUA’s age = 3x = 15 years. |
9. Sohail is younger than Rohan by 7 years. If their ages are in the respective ratio of 7:9, how old is Sohail? (a) 16 YEARS (b) 18 YEARS (c) 28 YEARS (d) 24.5 YEARS EXPLANATION: Let ROHAN’s age be x years. Then, SOHAIL’s age = (x – 7) years. x – 7 = 7 x 9 9x – 63 = 7x => 2x = 63 x = 31.5 Hence, SOHAIL’s age =(x – 7) = 24.5 years. |
9. Sohail is younger than Rohan by 7 years. If their ages are in the respective ratio of 7:9, how old is Sohail? (a) 16 YEARS (b) 18 YEARS (c) 28 YEARS (d) 24.5 YEARS EXPLANATION: Let ROHAN’s age be x years. Then, SOHAIL’s age = (x – 7) years. x – 7 = 7 x 9 9x – 63 = 7x => 2x = 63 x = 31.5 Hence, SOHAIL’s age =(x – 7) = 24.5 years. |
10. The present ages of three persons in proportions 4:7:9. Eight years ago, the sum of their ages was 56. Find their present ages (in years). (a) 8 , 20, 28 (b) 16 , 28, 36 (c) 20 , 35, 45 (d) NONE OF THESE EXPLANATION: Let their present ages be 4x, 7x and 9x years respectively. Then, (4x – 8) + (7x – 8) + (9x – 8) = 56 20x = 80 => x = 4. Their present ages are 4x = 16 years, 7x = 28 years and 9x = 36 years respectively. |
10. The present ages of three persons in proportions 4:7:9. Eight years ago, the sum of their ages was 56. Find their present ages (in years). (a) 8 , 20, 28 (b) 16 , 28, 36 (c) 20 , 35, 45 (d) NONE OF THESE EXPLANATION: Let their present ages be 4x, 7x and 9x years respectively. Then, (4x – 8) + (7x – 8) + (9x – 8) = 56 20x = 80 => x = 4. Their present ages are 4x = 16 years, 7x = 28 years and 9x = 36 years respectively. |