TEST - 5
1. Tanya’s grandfather was 8 times older to her 16 years ago. He would be 3 times of her age 8 years from now. What was ratio of ages of Tanya and her grandfather 8 years ago? (a) 11:50 (b) 11:51 (c) 11:53 (d) 11:54 REASON: Let, Tanya age 16 years ago = x, Grandfather’s age 16 years ago = 8x. 8 years from now, 3(x+16+8) = (8x+16+8) ==> 5x=48 => x = 48/5. |
1. Tanya’s grandfather was 8 times older to her 16 years ago. He would be 3 times of her age 8 years from now. What was ratio of ages of Tanya and her grandfather 8 years ago? (a) 11:50 (b) 11:51 (c) 11:53 (d) 11:54
REASON: Let, Tanya age 16 years ago = x, Grandfather’s age 16 years ago = 8x. 8 years from now, 3(x+16+8) = (8x+16+8) ==> 5x=48 => x = 48/5. |
2. A person’s present age is two-fifth of the age of his mother. After 8 years, he will be one-half of the age of his mother. How old is the mother at present (a) 38 (b) 40 (c) 42 (d) 44 REASON: Let the mother’s present age be x years. Then, the person’s present age = (2/5 x) years. => (2/5 x + 8/2) = 1 (x + 8) => 2(2x + 40) = 5(x + 8) => x = 40. |
2. A person’s present age is two-fifth of the age of his mother. After 8 years, he will be one-half of the age of his mother. How old is the mother at present (a) 38 (b) 40 (c) 42 (d) 44 REASON: Let the mother’s present age be x years. Then, the person’s present age = (2/5 x) years. => (2/5 x + 8/2) = 1 (x + 8) => 2(2x + 40) = 5(x + 8) => x = 40. |
3. 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) 15 years (b) 18 years (c) 20 years (d) 22 years REASON: Clue: (60 – x) – 6 = 5(x – 6). |
3. 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) 15 years (b) 18 years (c) 20 years (d) 22 years REASON: Clue: (60 – x) – 6 = 5(x – 6). |
4. Age of Umar will be 4 times the age of Raima in 6 years from today. If ages of Umar and Maryam are 7 times and 6 times the age of Raima respectively, what is present age of Umar? (a) 64 years (b) 30 years (c) 48 years (d) 42 years REASON: Let present age of Umar= U years, Maryam = M years and Raima= R years We know, U = 7R and M = 6R Also after 6 years, U+6=4(R+6) 7R+6=4R+24 R= 6 years = Present age of Raima Present age of Umar=7R=7×6=42 years. |
4. Age of Umar will be 4 times the age of Raima in 6 years from today. If ages of Umar and Maryam are 7 times and 6 times the age of Raima respectively, what is present age of Umar? (a) 64 years (b) 30 years (c) 48 years (d) 42 years REASON: Let present age of Umar= U years, Maryam = M years and Raima= R years We know, U = 7R and M = 6R Also after 6 years, U+6=4(R+6) 7R+6=4R+24 R= 6 years = Present age of Raima Present age of Umar=7R=7×6=42 years. |
5. Rohan’s age is five times ALI and seven-eighteenth of Meena’s age. The sum of the ages of all three of them is 132 years. How much younger is Ajay to Meena? (a) 56 years (b) 83 years (c) 27 years (d) Cannot be determined
REASON : Let, ALI’s age = A; So, Rohan’s age will be = 5 times ALI’s = 5A years Also, Rohan’s age=7/18 of Meena’s age Meena’s age= of Rohan’s age= 7 /18 x5A= 90A/ 7 years ALI’s age + Rohan’s age + Meena’s age = 132 A + 5A +90A/7=132 YEARS .7A+35A +90A = 132 x 7 .A=7 years=ALI’s age 90A Meena’s age=90 years ALI’S is (90-7=83) years younger than Meena |
5. Rohan’s age is five times ALI and seven-eighteenth of Meena’s age. The sum of the ages of all three of them is 132 years. How much younger is Ajay to Meena? (a) 56 years (b) 83 years (c) 27 years (d) Cannot be determined
REASON : Let, ALI’s age = A; So, Rohan’s age will be = 5 times ALI’s = 5A years Also, Rohan’s age=7/18 of Meena’s age Meena’s age= of Rohan’s age= 7 /18 x5A= 90A/ 7 years ALI’s age + Rohan’s age + Meena’s age = 132 A + 5A +90A/7=132 YEARS .7A+35A +90A = 132 x 7 .A=7 years=ALI’s age 90A Meena’s age=90 years ALI’S is (90-7=83) years younger than Meena |
6. The average age of 10 students and their teacher is 15 years. The average age of the first seven students is 15 yr and that of the last three is 11 yr. What is the teacher’s age? (a) 33 years (b) 30 years (c) 27 years (d) 24 years Let’s use algebra to solve this problem. The average age of 10 students and their teacher is 15 years= 10xstudents+1/11 = 15 Years The average age of the first seven students is 15 years: 7xstudent/7 = 15 The average age of the last three students is 11 years: 3xstudent/3 = 11 Sum of ages of the first seven students is 7 * 15 = 105 years. Sum of ages of the last three students is 3 * 11 = 33 years. Sum of ages of 10 students and teacher) / 11 = 15 Sum of ages of 10 students and teacher = 11 * 15 = 165 years Teacher’s age = (Ages of 10 students + teacher) – (Ages of first 7 students + Sum of ages of last 3 students) Teacher’s age = 165 – (105 + 33) = Teacher’s age = 165 – 138 Teacher’s age = 27 years |
6. The average age of 10 students and their teacher is 15 years. The average age of the first seven students is 15 yr and that of the last three is 11 yr. What is the teacher’s age? (a) 33 years (b) 30 years (c) 27 years (d) 24 years Let’s use algebra to solve this problem. The average age of 10 students and their teacher is 15 years= 10xstudents+1/11 = 15 Years The average age of the first seven students is 15 years: 7xstudent/7 = 15 The average age of the last three students is 11 years: 3xstudent/3 = 11 Sum of ages of the first seven students is 7 * 15 = 105 years. Sum of ages of the last three students is 3 * 11 = 33 years. Sum of ages of 10 students and teacher) / 11 = 15 Sum of ages of 10 students and teacher = 11 * 15 = 165 years Teacher’s age = (Ages of 10 students + teacher) – (Ages of first 7 students + Sum of ages of last 3 students) Teacher’s age = 165 – (105 + 33) = Teacher’s age = 165 – 138 Teacher’s age = 27 years |
7. Ramees and Shan’s average age is 65 years. The average age of Ramees, Shan and Junaid is 53 years. What is the age of Junaid? (a) 29 years (b) 31 years (c) 59 years (d) 45 years
Average age of Rameez & Shan = R+S/2=65 => R+S =130 Average age of Rameez, Shan & Junaid = R+S+J/3=53 => R+S+J = 159 Junaid= 159-130 = 29 Years. |
7. Ramees and Shan’s average age is 65 years. The average age of Ramees, Shan and Junaid is 53 years. What is the age of Junaid? (a) 29 years (b) 31 years (c) 59 years (d) 45 years
Average age of Rameez & Shan = R+S/2=65 => R+S =130 Average age of Rameez, Shan & Junaid = R+S+J/3=53 => R+S+J = 159 Junaid= 159-130 = 29 Years. |
8. The present ages of Amna and Nida are 59 and 37 years, respectively. What was the ratio of the ages of Nida and Amna 13 years ago? (a) 3:2 (b) 46:25 (c) 12:23 (d) 8:3
Present age of Amna = 59 years; Present age of Nida = 37 years 13 years ago: Amna’s age = 59 – 13 = 46 years Nida’s age = 37 – 13 = 24 years
Now finding ratio of Nida’s & Amna’s age 13 years ago: Ratio = Nida’s age / Amna’s age = 24 / 46 = 12/23. |
8. The present ages of Amna and Nida are 59 and 37 years, respectively. What was the ratio of the ages of Nida and Amna 13 years ago? (a) 3:2 (b) 46:25 (c) 12:23 (d) 8:3
Present age of Amna = 59 years; Present age of Nida = 37 years 13 years ago: Amna’s age = 59 – 13 = 46 years Nida’s age = 37 – 13 = 24 years
Now finding ratio of Nida’s & Amna’s age 13 years ago: Ratio = Nida’s age / Amna’s age = 24 / 46 = 12/23. |
9. Rohan is as much younger than Ahmed as he is older than Meena. The sum of ages of Ahmed and Meena is 108 years. How old is Rohan? (a) 32 years (b) 64 years (c) 52 years (d) 36 years
Rohan is younger than Ahmed as he is older than Meena: A – R = R – M The sum of ages of Ahmed and Meena is 108 years: A + M = 108 => A =108-M
We know; A – R = R – M => A = R + R – M => A = 2R – M A = 2R – M (putting value of A from above) 108-M=2R-M (M cancels out) 2R = 108 2R = 108 => 108 / 2 => 54. So, Rohan is 54 years old. |
9. Rohan is as much younger than Ahmed as he is older than Meena. The sum of ages of Ahmed and Meena is 108 years. How old is Rohan? (a) 32 years (b) 64 years (c) 52 years (d) 36 years
Rohan is younger than Ahmed as he is older than Meena: A – R = R – M The sum of ages of Ahmed and Meena is 108 years: A + M = 108 => A =108-M
We know; A – R = R – M => A = R + R – M => A = 2R – M A = 2R – M (putting value of A from above) 108-M=2R-M (M cancels out) 2R = 108 2R = 108 => 108 / 2 => 54. So, Rohan is 54 years old. |
10. Average age of a family of 4 members was 19 years, 4 years back. Birth of a new child kept the average age of the family same even today. How old is the child today?
(a) 4 years (b) 1 years (c) 2 years (d) 19 years
1. The average age of a family of 4 members was 19 years, 4 years ago: A = 19 2. The birth of a new child (B); The sum of ages of the 5 family members is (4A + C) According to question both averages are same hence; (4A + C) / 5 = A Putting value of A from the first equation (A = 19) into the second equation: (4 * 19 + C) / 5 = 19 76 + C = 19 * 5 76 + C = 95 C = 19 So, the child is 19 years old today. |
10. Average age of a family of 4 members was 19 years, 4 years back. Birth of a new child kept the average age of the family same even today. How old is the child today?
(a) 4 years (b) 1 years (c) 2 years (d) 19 years
1. The average age of a family of 4 members was 19 years, 4 years ago: A = 19 2. The birth of a new child (B); The sum of ages of the 5 family members is (4A + C) According to question both averages are same hence; (4A + C) / 5 = A Putting value of A from the first equation (A = 19) into the second equation: (4 * 19 + C) / 5 = 19 76 + C = 19 * 5 76 + C = 95 C = 19 So, the child is 19 years old today. |