📘 Quiz

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Question 1 / 20
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1
Rahul's father was 32 years older than Rahul's brother when Rahul was born, and his mother was 25 years older than Rahul's sister. Given that Rahul's brother is 6 years older than Rahul, and his mother is 3 years younger than his father, determine the age of Rahul's sister at the time of Rahul's birth.
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Solution: Step 1: When Rahul was born, his age was 0 years. Step 2: Since Rahul's brother is 6 years older than him, his brother's age when Rahul was born was 6 years. Step 3: Rahul's father was 32 years older than his brother at Rahul's birth. So, father's age at Rahul's birth = 6 + 32 = 38 years. Step 4: Rahul's mother is 3 years younger than his father. So, mother's age at Rahul's birth = 38 - 3 = 35 years. Step 5: Rahul's mother was 25 years older than his sister at Rahul's birth. So, sister's age at Rahul's birth = 35 - 25 = 10 years. Step 6: Therefore, Rahul's sister was 10 years old when he was born.
2
The sum of the current ages of Person X and Person Y is 48 years. If the ratio of their ages 15 years ago was 2:1, what will be the ratio of their ages 9 years from now?
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Solution: Step 1: Let current age of Person X = a years, Person Y = b years Step 2: Given: a + b = 48 Step 3: 15 years ago: (a - 15) / (b - 15) = 2/1 Step 4: Cross-multiply: a - 15 = 2(b - 15) Step 5: Expand: a - 15 = 2b - 30 Step 6: Rearrange: a - 2b = -15 Step 7: Solve system: a + b = 48 and a - 2b = -15 Step 8: From a + b = 48, express a: a = 48 - b Step 9: Substitute in a - 2b = -15: 48 - b - 2b = -15 Step 10: Combine: 48 - 3b = -15 Step 11: Solve for b: 3b = 63 → b = 21 Step 12: Find a: a = 48 - 21 = 27 Step 13: Ages 9 years later: X = 36, Y = 30 Step 14: Ratio = 36:30 = 6:5
3
A person's current age is two-fifths of their mother's age. In 8 years, the person's age will be one-half of the mother's age. What is the mother's current age?
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Solution: Step 1: Let the mother's present age be 'M' years. Step 2: The person's present age is (2/5)M years. Step 3: After 8 years, the mother's age will be (M + 8) years. Step 4: After 8 years, the person's age will be ((2/5)M + 8) years. Step 5: Formulate the equation based on the condition after 8 years: (2/5)M + 8 = (1/2)(M + 8). Step 6: Multiply by 10 (LCM of 5 and 2) to eliminate denominators: 10 * ((2/5)M + 8) = 10 * (1/2)(M + 8). Step 7: Simplify: 4M + 80 = 5(M + 8). Step 8: Expand: 4M + 80 = 5M + 40. Step 9: Solve for M: 80 - 40 = 5M - 4M. Step 10: M = 40 years. The mother's present age is 40 years.
4
A mother and her six children have an average age of 12 years. If the mother's age is removed, the average age of the children drops by 5 years. Determine the mother's age.
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Solution: Step 1: Calculate the total age of the mother and her six children. There are 1 (mother) + 6 (children) = 7 members. Total age = 12 years/person × 7 persons = 84 years. Step 2: Calculate the new average age of the children when the mother is excluded. New average = 12 years - 5 years = 7 years. Step 3: Calculate the total age of the six children. Total age = 7 years/child × 6 children = 42 years. Step 4: Find the mother's age by subtracting the children's total age from the family's total age. Mother's age = 84 years - 42 years = 42 years.
5
Q's age is equidistant from R's age and T's age (Q is younger than R by the same amount Q is older than T). If the total of R's and T's ages is 50 years, what is the exact difference between R's and Q's age?
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Solution: Step 1: Express the first condition: Q is as much younger than R as he is older than T. This translates to R - Q = Q - T. Step 2: Rearrange the equation from Step 1: R + T = 2Q. Step 3: Use the second condition: The sum of the ages of R and T is 50 years. So, R + T = 50. Step 4: Substitute R + T = 50 into the equation from Step 2: 50 = 2Q. Step 5: Solve for Q: Q = 50 / 2 = 25 years. Step 6: The question asks for the difference between R and Q's age, which is (R - Q). Step 7: While we know Q's age (25), we do not have sufficient information to determine R's age (or T's age individually, only their sum). For example, if R=30, T=20, then R-Q = 5. If R=40, T=10, then R-Q = 15. The difference varies. Step 8: Therefore, the difference between R and Q's age cannot be definitely determined from the given information.
6
A father was 24 years older than his son three years ago. Now, the father is five times as old as the son. How old will the son be three years from now?
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Solution: Step 1: Let the son's current age be x. Step 2: Three years ago, the son was x - 3 years old, and the father was (x - 3) + 24 years old. Step 3: The father's current age is (x - 3) + 24 + 3 = x + 24. Step 4: According to the problem, the father's current age is 5 times the son's current age: x + 24 = 5x. Step 5: Rearrange the equation: 24 = 5x - x, 24 = 4x. Step 6: Solve for x: x = 6. Step 7: The son's age three years from now will be 6 + 3 = 9 years.
7
Two siblings have an age difference of 8 years. Twelve years ago, the older sibling was twice as old as the younger one. What is the current age of the younger sibling?
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Solution: Step 1: Let younger sibling's age = x years Step 2: Older sibling's age = x + 8 years Step 3: Twelve years ago: Younger = x - 12, Older = (x + 8) - 12 = x - 4 Step 4: Set up equation: x - 4 = 2(x - 12) Step 5: Expand: x - 4 = 2x - 24 Step 6: Rearrange: 24 - 4 = 2x - x Step 7: Simplify: 20 = x Step 8: Younger sibling's current age = 20 years
8
Farah got married 8 years ago. Her current age is 9/7 times her age when she got married. Her daughter's current age is one-sixth of Farah's current age. What was her daughter's age 3 years prior to the present?
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Solution: Step 1: Let Farah's age at the time of her marriage (8 years ago) be 'x' years. Step 2: Farah's present age = (x + 8) years. Step 3: Formulate the equation based on the given ratio: x + 8 = (9/7) * x. Step 4: Multiply by 7 to clear the fraction: 7(x + 8) = 9x. Step 5: Expand and solve for x: 7x + 56 = 9x => 2x = 56 => x = 28. Step 6: Farah's present age = x + 8 = 28 + 8 = 36 years. Step 7: Daughter's present age = (1/6) * Farah's present age = (1/6) * 36 = 6 years. Step 8: Daughter's age 3 years ago = 6 - 3 = 3 years.
9
The sum of the current ages of a father and his son is 60 years. Six years ago, the father's age was five times his son's age. What will be the son's age after 6 more years from now?
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Solution: Step 1: Let the son's present age be 'x' years. Step 2: Since the sum of their present ages is 60, the father's present age = (60 - x) years. Step 3: Six years ago: Son's age = (x - 6) years. Father's age = (60 - x - 6) = (54 - x) years. Step 4: According to the problem, six years ago, the father's age was five times the son's age. Step 5: Set up the equation: (54 - x) = 5 * (x - 6). Step 6: 54 - x = 5x - 30. Step 7: Solve for x: 54 + 30 = 5x + x => 84 = 6x. Step 8: x = 84 / 6 => x = 14. Step 9: Son's present age = 14 years. Step 10: Son's age after 6 years (from present) = 14 + 6 = 20 years.
10
Rahul is younger than Sagar by the same amount that he is older than Purav. If the total of Purav's and Sagar's ages is 66 years, and Sagar is 48 years old, what is the difference in age between Rahul and Purav?
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Solution: Step 1: Let the age of Rahul be R, Sagar be S, and Purav be P. Step 2: Translate the first condition: "Rahul is as much younger than Sagar as he is older than Purav." This translates to: S - R = R - P. Step 3: Rearrange the equation: S + P = 2R. This means Rahul's age is the average of Sagar's and Purav's ages. Step 4: Use the given information: The sum of the ages of Purav and Sagar is 66 years, so P + S = 66. Step 5: Substitute this sum into the rearranged equation from Step 3: 66 = 2R R = 66 / 2 = 33 years (Rahul's age). Step 6: Use Sagar's given age: S = 48 years. Step 7: Use the sum (P + S = 66) to find Purav's age: P + 48 = 66 P = 66 - 48 = 18 years (Purav's age). Step 8: Calculate the difference between Rahul's and Purav's age: R - P = 33 - 18 = 15 years.
11
Mr. Joe's family includes himself, his wife, and their four children. The average family age immediately after the birth of the first, second, third, and fourth child was 16, 15, 16, and 15 years, respectively. Given that the current average age of the entire six-person family is 16 years, what is the age of Mr. Joe's eldest son?
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Solution: Step 1: At 1st child's birth (3 members): Total age = 16 * 3 = 48 years. Step 2: At 2nd child's birth (4 members): Total age = 15 * 4 = 60 years. Step 3: Time elapsed between 1st and 2nd child's birth = (60 - 48) / 3 = 12 / 3 = 4 years. Eldest son's age at 2nd child's birth = 4 years. Step 4: At 3rd child's birth (5 members): Total age = 16 * 5 = 80 years. Step 5: Time elapsed between 2nd and 3rd child's birth = (80 - 60) / 4 = 20 / 4 = 5 years. Eldest son's age at 3rd child's birth = 4 + 5 = 9 years. Step 6: At 4th child's birth (6 members): Total age = 15 * 6 = 90 years. Step 7: Time elapsed between 3rd and 4th child's birth = (90 - 80) / 5 = 10 / 5 = 2 years. Eldest son's age at 4th child's birth = 9 + 2 = 11 years. Step 8: At Present (6 members): Total age = 16 * 6 = 96 years. Step 9: Time elapsed between 4th child's birth and present = (96 - 90) / 6 = 6 / 6 = 1 year. Step 10: Present age of eldest son = 11 + 1 = 12 years.
12
The ages of a husband, wife, and their child are in the ratio 13 : 11 : 3. If the average age of the family is 36 years, what is the difference in age between the husband and wife?
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Solution: Step 1: Ages in ratio = 13 : 11 : 3 Step 2: Total parts = 13 + 11 + 3 = 27p Step 3: Average age = 36 years Step 4: Total age = 36 * 3 = 108 years Step 5: 27p = 108 Step 6: 1p = 4 Step 7: Husband's age = 13p = 13 * 4 = 52 years Step 8: Wife's age = 11p = 11 * 4 = 44 years Step 9: Difference in age = 52 - 44 = 8 years
13
The average age of four boys, A, B, C, and D, is 5 years. The average age of A, B, D, and E is 6 years. Given that C is 8 years old, what is the age of E?
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Solution: Step 1: From the first statement, the total age of A, B, C, and D is: 4 members × 5 years/member = 20 years (A + B + C + D = 20). Step 2: From the second statement, the total age of A, B, D, and E is: 4 members × 6 years/member = 24 years (A + B + D + E = 24). Step 3: Substitute C's age (8 years) into the first equation: A + B + 8 + D = 20. Step 4: Simplify to find the sum of A, B, and D: A + B + D = 20 - 8 = 12 years. Step 5: Substitute the sum (A + B + D = 12) into the second equation: 12 + E = 24. Step 6: Solve for E: E = 24 - 12 = 12 years.
14
The average age of three boys is 15 years. If their ages are in the ratio 3:5:7, what is the age of the youngest boy?
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Solution: Step 1: Calculate the total age of the three boys: Total age = Average age * Number of boys = 15 years * 3 = 45 years. Step 2: Represent the ages of the boys using the given ratio. Let their ages be 3x, 5x, and 7x. Step 3: Set up an equation using the total age: 3x + 5x + 7x = 45. Step 4: Combine the terms: 15x = 45. Step 5: Solve for x: x = 45 / 15 = 3. Step 6: Determine the age of the youngest boy, which corresponds to the smallest ratio part (3x): Youngest boy's age = 3 * 3 = 9 years.
15
Five years ago, the average age of A, B, C, and D was 45 years. Now, with E joining them, the average age of all five individuals is 49 years. What is E's current age?
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Solution: Step 1: Calculate the total age of A, B, C, and D five years ago: Total_age_past = 4 people * 45 years/person = 180 years. Step 2: Calculate their current total age. Each of the 4 people has aged 5 years, so their combined age increased by 4 * 5 = 20 years. Total_current_age_ABCD = 180 years + 20 years = 200 years. Step 3: After E joins, there are 5 people, and their average age is 49 years. Step 4: Calculate the total current age of all five individuals (A, B, C, D, and E): Total_current_age_ABCDE = 5 people * 49 years/person = 245 years. Step 5: The age of E is the difference between the total current age of five people and the total current age of A, B, C, and D. Age of E = Total_current_age_ABCDE - Total_current_age_ABCD = 245 years - 200 years = 45 years.
16
15 years ago, Person A was three times as old as Person B. Now, Person A is only twice as old as Person B. What is the sum of their current ages?
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Solution: Step 1: Let Person B's current age = x years Step 2: Person A's current age = 2x years Step 3: 15 years ago, Person A's age = 2x - 15 Step 4: 15 years ago, Person B's age = x - 15 Step 5: Set up equation: 2x - 15 = 3(x - 15) Step 6: Expand: 2x - 15 = 3x - 45 Step 7: Rearrange: 45 - 15 = 3x - 2x Step 8: Simplify: 30 = x Step 9: Sum of current ages = 2x + x = 3x = 3*30 = 90 years
17
A person's mother was four times their age 12 years ago. In 12 years, she will be twice as old as the person. What is the mother's current age?
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Solution: Step 1: Let person's current age = x years Step 2: Mother's age 12 years ago = 4(x - 12) Step 3: Mother's current age = 4x - 48 + 12 = 4x - 36 Step 4: Person's age in 12 years = x + 12 Step 5: Mother's age in 12 years = 4x - 24 Step 6: Set equation: 4x - 24 = 2(x + 12) Step 7: Solve: 4x - 2x = 24 + 24 Step 8: Simplify: 2x = 48 → x = 24 Step 9: Mother's current age = 4(24) - 36 = 60 years
18
Five years ago, the total age of a group of 6 individuals was 182 years. Two years later, one member passed away at 50, and a child was born. After another 2 years, another member died at 40, and another child was born. What is the current average age of the group?
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Solution: Step 1: 5 years ago, total age = 182 years Step 2: 2 years later, total age = 182 + 6*2 - 50 = 142 (child born) Step 3: After another 2 years, total age = 142 + 6*2 - 40 = 114 (another child born) Step 4: Current total age = 114 + 6*1 = 120 Step 5: Current average age = 120 / 6 = 20 years
19
A father states to his son, "At the time of your birth, my age was the same as your current age." If the father's present age is 38 years, what was the son's age five years ago?
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Solution: Step 1: Let the son's present age be 'x' years. Step 2: The father's present age is 38 years. Step 3: The father's statement implies that the father's age at the son's birth was 'x' years. Step 4: The difference between the father's age and the son's age remains constant throughout their lives. Step 5: At the son's birth, his age was 0. So, the age difference was (Father's age at birth) - 0 = x. Step 6: At present, the age difference is (Father's present age) - (Son's present age) = 38 - x. Step 7: Equate the age differences: x = 38 - x. Step 8: Solve for x: 2x = 38 => x = 19. Step 9: The son's present age is 19 years. Step 10: To find the son's age five years back, subtract 5 from his present age: 19 - 5 = 14 years.
20
What will be the ratio of Sam's age to Albert's age in 5 years? I. Sam's current age exceeds Albert's current age by 4 years. II. Albert's current age is 20 years. III. The ratio of Albert's current age to Sam's current age is 5:6.
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Solution: Step 1: Let Sam's present age be S and Albert's present age be A. We need to find the ratio (S+5) : (A+5). Step 2: Formulate equations: From I: S = A + 4 (Eq 1) From II: A = 20 (Eq 2) From III: A / S = 5 / 6 => 6A = 5S (Eq 3) Step 3: Check combinations for sufficiency: * **I and II:** From (2), A=20. Substitute into (1): S = 20 + 4 = 24. So, S=24, A=20. Ages after 5 years: S+5=29, A+5=25. Ratio = 29:25. Sufficient. * **II and III:** From (2), A=20. Substitute into (3): 6(20) = 5S => 120 = 5S => S = 24. So, S=24, A=20. Ages after 5 years: S+5=29, A+5=25. Ratio = 29:25. Sufficient. * **I and III:** From (1), S = A + 4. Substitute into (3): 6A = 5(A + 4) => 6A = 5A + 20 => A = 20. Then S = 20 + 4 = 24. So, S=24, A=20. Ages after 5 years: S+5=29, A+5=25. Ratio = 29:25. Sufficient. Step 4: Conclusion: Any two of the three statements are sufficient to determine the ratio between Sam and Albert's ages after 5 years.
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