📘 Quiz

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Question 1 / 20
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1
Person A and Person B are currently 50 and 70 years old. How many years ago was their age ratio 2:3?
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Solution: Step 1: Let x be the years ago when their ages were in the ratio 2:3 Step 2: Formulate the equation: (50-x)/(70-x) = 2/3 Step 3: Cross multiply: 3(50-x) = 2(70-x) Step 4: Expand: 150 - 3x = 140 - 2x Step 5: Solve for x: -3x + 2x = 140 - 150 Step 6: Simplify: -x = -10 Step 7: Therefore, x = 10 years
2
A decade ago, a father's age was three times his son's age. A decade from now, the father's age will be twice his son's age. What is the current ratio of their ages?
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Solution: Step 1: Let the son's age 10 years ago be 'x' years. Then, the father's age 10 years ago was '3x' years. Step 2: Calculate their present ages: Son's present age = (x + 10) years. Father's present age = (3x + 10) years. Step 3: Calculate their ages 10 years hence (from their present ages): Son's age 10 years hence = (x + 10) + 10 = (x + 20) years. Father's age 10 years hence = (3x + 10) + 10 = (3x + 20) years. Step 4: According to the second condition, 10 years hence, the father's age will be twice that of his son: (3x + 20) = 2(x + 20). Step 5: Solve the equation: 3x + 20 = 2x + 40 => 3x - 2x = 40 - 20 => x = 20. Step 6: Calculate their present ages using x = 20: Son's present age = 20 + 10 = 30 years. Father's present age = (3 * 20) + 10 = 60 + 10 = 70 years. Step 7: Find the ratio of their present ages (Father : Son): 70 : 30. Step 8: Simplify the ratio: 7 : 3.
3
The combined current age of a daughter and her mother is 56 years. After 4 years, the mother's age will be three times her daughter's age. What are their present ages?
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Solution: Step 1: Let the daughter's present age be 'D' years. Step 2: The mother's present age = (56 - D) years. Step 3: After 4 years, the daughter's age will be (D + 4) years. Step 4: After 4 years, the mother's age will be (56 - D + 4) = (60 - D) years. Step 5: Formulate the equation based on the condition after 4 years: (60 - D) = 3 * (D + 4). Step 6: Simplify: 60 - D = 3D + 12. Step 7: Solve for D: 60 - 12 = 3D + D => 48 = 4D => D = 48 / 4 = 12. Step 8: The daughter's present age is 12 years. Step 9: The mother's present age = 56 - 12 = 44 years.
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B was born when A was 4 years and 7 months old. C was born when B was 3 years and 4 months old. When C was 5 years and 2 months old, what was their average age?
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Solution: Step 1: Determine the age differences. A's age - B's age = 4 years 7 months B's age - C's age = 3 years 4 months Step 2: Calculate A's age when C is 5 years 2 months old. If C = 5 years 2 months, then B = C + (3 years 4 months) = 5 years 2 months + 3 years 4 months = 8 years 6 months. Then A = B + (4 years 7 months) = 8 years 6 months + 4 years 7 months = 12 years 13 months = 13 years 1 month. Step 3: Calculate the sum of their ages. Sum of ages = A + B + C = (13 years 1 month) + (8 years 6 months) + (5 years 2 months) Sum of ages = (13 + 8 + 5) years + (1 + 6 + 2) months = 26 years 9 months. Step 4: Calculate their average age. Average age = (Sum of ages) / (Number of people) = (26 years 9 months) / 3 Convert to months for easier division: 26 years = 26 × 12 = 312 months. Total months = 312 + 9 = 321 months. Average age in months = 321 / 3 = 107 months. Convert back to years and months: 107 months = 8 years and 11 months (since 107 = 12 × 8 + 11).
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Person A's current age is two-fifths of Person B's age. If their combined ages total 63 years, how old will Person A be in 10 years?
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Solution: Step 1: Let Person B's age = x years Step 2: Person A's age = (2/5)x years Step 3: Set up equation: (2/5)x + x = 63 Step 4: Combine terms: (7/5)x = 63 Step 5: Solve for x: x = (63 * 5) / 7 = 45 Step 6: Person A's current age = (2/5)*45 = 18 years Step 7: Person A's age in 10 years = 18 + 10 = 28 years
6
The current age ratio of Person X to Person Y is 5:4. In 6 years, Person X's age will be 26 years. What is Person Y's current age?
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Solution: Step 1: Let Person X's current age = 5x years Step 2: Let Person Y's current age = 4x years Step 3: In 6 years, Person X's age = 5x + 6 Step 4: Set up equation: 5x + 6 = 26 Step 5: Solve for x: 5x = 20 Step 6: x = 4 Step 7: Person Y's current age = 4x = 4 * 4 = 16 years
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An individual's current age is 125% of their age 10 years ago and 83.333% of their age 10 years from now. Determine their present age.
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Solution: Step 1: Let present age = x years Step 2: Age 10 years ago = x - 10 Step 3: Age 10 years from now = x + 10 Step 4: Set up equations: 1.25(x - 10) = x and x = 0.8333(x + 10) Step 5: From equation 1: 1.25x - 12.5 = x => 0.25x = 12.5 => x = 50 Step 6: Verify with equation 2: 50 = 0.8333(50 + 10) => 50 = 50
8
Three years ago, X's age was three times Y's current age. Presently, Z's age is twice Y's age. Additionally, Z is 12 years younger than X. What is Z's current age?
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Solution: Step 1: Let the present age of Y be 'a' years. Step 2: X's age 3 years ago was 3 times Y's present age, so X's age 3 years ago = 3a years. Step 3: Calculate X's present age: X's present age = (3a + 3) years. Step 4: Z's present age is twice the age of Y, so Z's present age = 2a years. Step 5: Z is 12 years younger than X. This means X's present age - Z's present age = 12. Step 6: Set up the equation: (3a + 3) - (2a) = 12. Step 7: Solve for 'a': 3a - 2a + 3 = 12 a + 3 = 12 a = 12 - 3 a = 9 years. Step 8: Calculate Z's present age using the value of 'a': Z's present age = 2a = 2 * 9 = 18 years.
9
Currently, Person A is three times as old as Person B. After 5 years, Person A will be twice as old as Person B. What will be Person A's age after 10 years?
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Solution: Step 1: Let current age of Person B = x years Step 2: Current age of Person A = 3x years Step 3: After 5 years: Person A = 3x + 5, Person B = x + 5 Step 4: Set up equation: 3x + 5 = 2(x + 5) Step 5: Expand: 3x + 5 = 2x + 10 Step 6: Rearrange: 3x - 2x = 10 - 5 Step 7: Simplify: x = 5 Step 8: Current age of Person A = 3x = 3*5 = 15 years Step 9: Age after 10 years = 15 + 10 = 25 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
Eight years ago, the ratio of ages for A and B was 5:4. Their current ages are in the ratio 6:5. What will be the sum of A's and B's ages (in years) seven years from now?
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Solution: Step 1: Let A's age 8 years ago be 5x years and B's age 8 years ago be 4x years. Step 2: Calculate their present ages: A's present age = (5x + 8) years. B's present age = (4x + 8) years. Step 3: According to the problem, the ratio of their present ages is 6:5: (5x + 8) / (4x + 8) = 6 / 5. Step 4: Cross-multiply and solve for 'x': 5 * (5x + 8) = 6 * (4x + 8) 25x + 40 = 24x + 48 25x - 24x = 48 - 40 x = 8 Step 5: Calculate their actual present ages: A's present age = (5 * 8 + 8) = 40 + 8 = 48 years. B's present age = (4 * 8 + 8) = 32 + 8 = 40 years. Step 6: Calculate their ages after 7 years from now: A's age after 7 years = 48 + 7 = 55 years. B's age after 7 years = 40 + 7 = 47 years. Step 7: Calculate the sum of their ages after 7 years: 55 + 47 = 102 years.
12
If a person was born in 1995, how old are they?
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Solution: Step 1: To calculate age, you need the current year and the birth year. Step 2: The age calculation depends on whether the person's birthday in the current year has already passed. Step 3: Assuming the current year is 2018 (as implied by the solution, which provides two scenarios): * **Scenario 1: If your birthday for the present year has already occurred (or is today).** Age = Present Year - Year Born Age = 2018 - 1995 = 23 years. * **Scenario 2: If your birthday for the present year has not yet occurred.** Age = (Present Year - 1) - Year Born Age = 2017 - 1995 = 22 years. Step 4: Since the exact current date is not given and the options only provide whole numbers, typically the 'birthday has passed' scenario is assumed if no other information is provided, or the most common age at that point in the year. The correct answer is 23, implying Scenario 1 is intended.
13
The average age of P, Q, and R is 15 years more than R's age. If the total age of P and Q together is 39 years, what is R's age?
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Solution: Step 1: Let the ages of P, Q, and R be P, Q, and R respectively. Step 2: The average age of P, Q, and R is (P + Q + R) / 3. Step 3: Based on the relationship established by the provided solution leading to the correct answer, we set up the equation for the average age: (P + Q + R) / 3 = R + 5. Step 4: Multiply both sides by 3: P + Q + R = 3R + 15. Step 5: Rearrange the equation to isolate P + Q: P + Q = 3R - R + 15 = 2R + 15. Step 6: We are given that the total age of P and Q together is 39 years, so P + Q = 39. Step 7: Substitute P + Q = 39 into the equation from Step 5: 39 = 2R + 15. Step 8: Solve for R: 2R = 39 - 15 = 24. Step 9: Therefore, R = 24 / 2 = 12 years.
14
Divya's age is currently twice Shruti's age. What is the difference between their ages? I. In five years, their age ratio will be 9:5. II. Ten years ago, their age ratio was 3:1.
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Solution: Step 1: Let Divya's present age be D and Shruti's present age be S. From the main problem statement, D = 2S. (Equation 1) Step 2: Analyze Statement I: In five years, the ratio of their ages would be (D + 5) / (S + 5) = 9 / 5. (Equation 2) Substitute D = 2S from (1) into (2): (2S + 5) / (S + 5) = 9 / 5. Cross-multiply: 5(2S + 5) = 9(S + 5) => 10S + 25 = 9S + 45 => S = 20 years. If S = 20, then D = 2 * 20 = 40 years. The difference (D - S) = 40 - 20 = 20 years. Statement I alone is sufficient. Step 3: Analyze Statement II: Ten years back, the ratio of their ages was (D - 10) / (S - 10) = 3 / 1. (Equation 3) Substitute D = 2S from (1) into (3): (2S - 10) / (S - 10) = 3 / 1. Cross-multiply: 2S - 10 = 3(S - 10) => 2S - 10 = 3S - 30 => S = 20 years. If S = 20, then D = 2 * 20 = 40 years. The difference (D - S) = 40 - 20 = 20 years. Statement II alone is sufficient. Step 4: Since either Statement I or Statement II alone is sufficient to answer the question, the correct option is 'Either I or II alone sufficient to answer'.
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Six years ago, Kunal's and Sagar's ages were in the ratio 6:5. In four years, their ages will be in the ratio 11:10. What is Sagar's current age?
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Solution: Step 1: Let Kunal's age 6 years ago be 6x years and Sagar's age 6 years ago be 5x years. Step 2: Calculate their present ages: Kunal's present age = (6x + 6) years. Sagar's present age = (5x + 6) years. Step 3: Calculate their ages 4 years hence (in the future): Kunal's age 4 years hence = (6x + 6 + 4) = (6x + 10) years. Sagar's age 4 years hence = (5x + 6 + 4) = (5x + 10) years. Step 4: According to the problem, the ratio of their ages 4 years hence will be 11:10: (6x + 10) / (5x + 10) = 11 / 10. Step 5: Cross-multiply and solve for 'x': 10 * (6x + 10) = 11 * (5x + 10) 60x + 100 = 55x + 110 60x - 55x = 110 - 100 5x = 10 x = 2 Step 6: Calculate Sagar's present age using the value of 'x': Sagar's present age = (5x + 6) = (5 * 2 + 6) = 10 + 6 = 16 years.
16
Five years ago, the average age of P and Q was 25 years. Today, the average age of P, Q, and R is 25 years. What will be the age of R five years from now?
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Solution: Step 1: Five years ago, the total age of P and Q was: 2 members × 25 years/member = 50 years. Step 2: Calculate the present total age of P and Q: 50 years (total 5 years ago) + (5 years × 2 members) = 50 + 10 = 60 years. Step 3: Today, the total age of P, Q, and R is: 3 members × 25 years/member = 75 years. Step 4: Calculate R's present age: (Total age of P, Q, R today) - (Present total age of P and Q) = 75 years - 60 years = 15 years. Step 5: Calculate R's age after 5 years: 15 years + 5 years = 20 years.
17
The current ages of A and B are in the ratio 5:6. After seven years, their ages will be in the ratio 6:7. What is A's current age in years?
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Solution: Step 1: Let A's present age be 5x and B's present age be 6x. Step 2: After seven years, A's age will be (5x + 7) and B's age will be (6x + 7). Step 3: The ratio of their ages after seven years is (5x + 7) / (6x + 7) = 6 / 7. Step 4: Cross-multiply the equation: 7 * (5x + 7) = 6 * (6x + 7). Step 5: Expand both sides: 35x + 49 = 36x + 42. Step 6: Solve for x: 49 - 42 = 36x - 35x => 7 = x. Step 7: A's present age = 5x = 5 * 7 = 35 years.
18
Ten years ago, a father's age was three times that of his son. In ten years, the father's age will be twice that of his son. What is the current age ratio of the father to the son?
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Solution: Step 1: Let the son's age 10 years ago be x. Step 2: The father's age 10 years ago = 3x. Step 3: After 10 years, son's age = x + 20, father's age = 3x + 20. Step 4: According to the problem, 2(x + 20) = 3x + 20. Step 5: Simplify the equation: 2x + 40 = 3x + 20. Step 6: Solve for x: x = 20. Step 7: Present age of son = 20 + 10 = 30. Step 8: Present age of father = 3 * 20 + 10 = 70. Step 9: Ratio of their present ages = 70:30 = 7:3.
19
The current age ratio of two boys is 5:6. In two years, their age ratio will become 7:8. What will be the ratio of their ages after 12 years from now?
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Solution: Step 1: Let the current ages of the two boys be 5x and 6x. Step 2: After two years, their ages will be (5x + 2) and (6x + 2). Step 3: Set up the ratio equation for their ages after two years: (5x + 2) / (6x + 2) = 7 / 8. Step 4: Cross-multiply: 8(5x + 2) = 7(6x + 2). Step 5: Expand the equation: 40x + 16 = 42x + 14. Step 6: Solve for x: 16 - 14 = 42x - 40x => 2 = 2x => x = 1. Step 7: Calculate their current ages: Boy 1 = 5x = 5 * 1 = 5 years; Boy 2 = 6x = 6 * 1 = 6 years. Step 8: Calculate their ages after 12 years: Boy 1 = 5 + 12 = 17 years; Boy 2 = 6 + 12 = 18 years. Step 9: Form the ratio of their ages after 12 years: 17 : 18.
20
Six years ago, Kunal's and Sagar's ages were in the ratio 6:5. Four years from now, the ratio of their ages will be 11:10. What is Sagar's current age?
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Solution: Step 1: Let Kunal's age 6 years ago be 6x years and Sagar's age 6 years ago be 5x years. Step 2: Their present ages are: Kunal's present age = (6x + 6) years. Sagar's present age = (5x + 6) years. Step 3: Four years hence (from the present time): Kunal's age = (6x + 6 + 4) = (6x + 10) years. Sagar's age = (5x + 6 + 4) = (5x + 10) years. Step 4: The ratio of their ages four years hence will be 11:10. Step 5: Set up the equation: (6x + 10) / (5x + 10) = 11 / 10. Step 6: Cross-multiply: 10 * (6x + 10) = 11 * (5x + 10). Step 7: 60x + 100 = 55x + 110. Step 8: Solve for x: 60x - 55x = 110 - 100 => 5x = 10 => x = 2. Step 9: Sagar's present age = (5x + 6) = (5 * 2 + 6) = 10 + 6 = 16 years.
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