Question 1

Vikram's age is 3 years more than twice Isha's age. If Vikram is currently 21 years old, what is Isha's current age?

Accepted Answer

Step 1: Let Isha's current age = x years. Step 2: Vikram's age = 2x + 3 years. Step 3: Given Vikram's age = 21, so 2x + 3 = 21. Step 4: 2x = 21 - 3 = 18. Step 5: x = 18 ÷ 2 = 9. Step 6: Isha's current age = 9 years.

Question 2

The ratio of Ravi's age to Sita's age is 7:5. If Ravi is 14 years older than Sita, what will be the ratio of their ages after 10 years?

Accepted Answer

Step 1: Let Ravi's age = 7x and Sita's age = 5x. Step 2: Given Ravi is 14 years older, so 7x - 5x = 14. Step 3: 2x = 14, therefore x = 7. Step 4: Ravi's current age = 7(7) = 49 years and Sita's current age = 5(7) = 35 years. Step 5: After 10 years, Ravi's age = 49 + 10 = 59 years and Sita's age = 35 + 10 = 45 years. Step 6: Ratio after 10 years = 59:45. Step 7: Simplify by finding GCD(59, 45) = 1, so ratio remains 59:45.

Question 3

The ratio of ages of Aman, Bimal, and Chetan is 2:3:4. If the sum of their ages is 54 years, what is Chetan's age?

Accepted Answer

Step 1: Let Aman's age = 2x, Bimal's age = 3x, and Chetan's age = 4x. Step 2: Sum of ages = 2x + 3x + 4x = 9x = 54. Step 3: x = 54 ÷ 9 = 6. Step 4: Chetan's age = 4x = 4(6) = 24 years.

Question 4

The ratio of the present ages of Arun and Bhavna is 5:3. If Arun is 10 years older than Bhavna, what will be the ratio of their ages after 6 years?

Accepted Answer

Step 1: Let Arun's present age = 5x and Bhavna's present age = 3x. Step 2: Given that Arun is 10 years older than Bhavna, so 5x - 3x = 10, which gives 2x = 10, thus x = 5. Step 3: Arun's present age = 5(5) = 25 years and Bhavna's present age = 3(5) = 15 years. Step 4: After 6 years, Arun's age = 25 + 6 = 31 years and Bhavna's age = 15 + 6 = 21 years. Step 5: Ratio after 6 years = 31:21. Therefore, the answer is 31:21.

Question 5

The ratio of the present ages of Arun and Bhavna is 5:3. If Arun is 10 years older than Bhavna, what will be the ratio of their ages after 6 years?

Accepted Answer

Step 1: Let Arun's present age = 5x and Bhavna's present age = 3x. Step 2: Given that Arun is 10 years older than Bhavna, so 5x - 3x = 10, which gives 2x = 10, therefore x = 5. Step 3: Arun's present age = 5(5) = 25 years and Bhavna's present age = 3(5) = 15 years. Step 4: After 6 years, Arun's age = 25 + 6 = 31 years and Bhavna's age = 15 + 6 = 21 years. Step 5: Ratio after 6 years = 31:21. Therefore, the answer is 31:21.

Question 6

The ratio of the present ages of Arun and Bhavna is 5:3. If Arun is 20 years older than Bhavna, what is Bhavna's present age?

Accepted Answer

Step 1: Let Arun's age = 5x and Bhavna's age = 3x (from ratio 5:3). Step 2: Given that Arun is 20 years older than Bhavna, so 5x - 3x = 20. Step 3: 2x = 20, therefore x = 10. Step 4: Bhavna's age = 3x = 3(10) = 30 years.

Question 7

The ratio of the ages of Ram and Shyam is 3:5. If Ram is 18 years old, what is the age of Shyam?

Accepted Answer

Step 1: Let Ram's age = 3x and Shyam's age = 5x. Step 2: Given Ram's age = 18, so 3x = 18, which gives x = 6. Step 3: Shyam's age = 5x = 5 × 6 = 30 years. Therefore, the answer is 30 years.

Question 8

The present ages of Aman and Bina are in the ratio 3:2. Six years from now, the ratio of their ages will be 5:4. What is the difference between their current ages?

Accepted Answer

Step 1: Let Aman's current age = 3x and Bina's current age = 2x (from ratio 3:2). Step 2: After 6 years, Aman's age = 3x + 6 and Bina's age = 2x + 6. Step 3: Given that after 6 years the ratio is 5:4, so (3x + 6)/(2x + 6) = 5/4. Step 4: Cross-multiply: 4(3x + 6) = 5(2x + 6). Step 5: 12x + 24 = 10x + 30. Step 6: 12x - 10x = 30 - 24. Step 7: 2x = 6, so x = 3. Step 8: Aman's current age = 3(3) = 9 years, Bina's current age = 2(3) = 6 years. Step 9: Difference = 9 - 6 = 3 years.

Question 9

Five years ago, the ratio of Priya's age to Deepak's age was 3:2. If Deepak is currently 30 years old, what is Priya's current age?

Accepted Answer

Step 1: Deepak's current age = 30 years. Step 2: Deepak's age 5 years ago = 30 - 5 = 25 years. Step 3: Ratio 5 years ago was Priya:Deepak = 3:2. Step 4: If Deepak's age 5 years ago = 25, then 25 corresponds to the '2' part of the ratio. Step 5: One ratio unit = 25 ÷ 2 = 12.5 years. Step 6: Priya's age 5 years ago = 3 × 12.5 = 37.5 years. Step 7: Priya's current age = 37.5 + 5 = 42.5 years.

Question 10

The ratio of Ravi's age to Sita's age is 7:5. After 6 years, their ages will be in the ratio 4:3. What is Ravi's current age?

Accepted Answer

Step 1: Let Ravi's current age = 7x and Sita's current age = 5x (from ratio 7:5). Step 2: After 6 years, Ravi's age = 7x + 6 and Sita's age = 5x + 6. Step 3: Given that after 6 years the ratio is 4:3, so (7x + 6)/(5x + 6) = 4/3. Step 4: Cross-multiply: 3(7x + 6) = 4(5x + 6). Step 5: 21x + 18 = 20x + 24. Step 6: 21x - 20x = 24 - 18. Step 7: x = 6. Step 8: Ravi's current age = 7x = 7(6) = 42 years.

Question 11

Meera's age is 4 times Neha's age. After 8 years, Meera's age will be 2 times Neha's age. What is Neha's current age?

Accepted Answer

Step 1: Let Neha's current age = x years. Then Meera's current age = 4x years. Step 2: After 8 years, Neha's age = x + 8 and Meera's age = 4x + 8. Step 3: Given that after 8 years, Meera's age = 2 × Neha's age, so 4x + 8 = 2(x + 8). Step 4: 4x + 8 = 2x + 16. Step 5: 2x = 8, therefore x = 4. Step 6: Neha's current age = 4 years.

Question 12

The ratio of the present ages of A and B is 3:5. After 10 years, the ratio of their ages will be 5:7. What is the present age of B?

Accepted Answer

Step 1: Let present ages of A and B be 3x and 5x respectively. Step 2: After 10 years: (3x + 10)/(5x + 10) = 5/7. Step 3: Cross multiply: 7(3x + 10) = 5(5x + 10) → 21x + 70 = 25x + 50 → 4x = 20 → x = 5. Step 4: Present age of B = 5x = 5 × 5 = 25 years. Therefore, answer is 25 years.

Question 13

The ratio of the present ages of Arun and Bhavna is 5:7. Four years ago, the ratio of their ages was 3:5. What will be the ratio of their ages after 8 years?

Accepted Answer

Step 1: Let present ages be Arun = 5x and Bhavna = 7x. Step 2: Four years ago, ages were (5x - 4) and (7x - 4), with ratio 3:5. Step 3: Set up equation: (5x - 4)/(7x - 4) = 3/5. Step 4: Cross multiply: 5(5x - 4) = 3(7x - 4) → 25x - 20 = 21x - 12 → 4x = 8 → x = 2. Step 5: Present ages: Arun = 10, Bhavna = 14. Step 6: After 8 years: Arun = 18, Bhavna = 22. Step 7: Ratio = 18:22 = 9:11.

Question 14

The ratio of ages of Mohan and Sohan is currently 3:2. After 8 years, the ratio will be 5:4. What will be the ratio of their ages after 16 years?

Accepted Answer

Step 1: Let Mohan's present age = 3x and Sohan's present age = 2x. Step 2: After 8 years, Mohan's age = 3x + 8 and Sohan's age = 2x + 8. Step 3: Given (3x + 8):(2x + 8) = 5:4. Step 4: Cross-multiply: 4(3x + 8) = 5(2x + 8). Step 5: 12x + 32 = 10x + 40. Step 6: 2x = 8, so x = 4. Step 7: Mohan's present age = 3(4) = 12 years and Sohan's present age = 2(4) = 8 years. Step 8: After 16 years, Mohan's age = 12 + 16 = 28 years and Sohan's age = 8 + 16 = 24 years. Step 9: Ratio = 28:24 = 7:6.

Question 15

The ratio of the present ages of Arun and Bhavna is 5:3. After 6 years, the ratio of their ages will be 7:5. What is Arun's present age?

Accepted Answer

Step 1: Let Arun's present age = 5x and Bhavna's present age = 3x. Step 2: After 6 years, Arun's age = 5x + 6 and Bhavna's age = 3x + 6. Step 3: Given that (5x + 6):(3x + 6) = 7:5. Step 4: Cross-multiply: 5(5x + 6) = 7(3x + 6). Step 5: 25x + 30 = 21x + 42. Step 6: 4x = 12, so x = 3. Step 7: Arun's present age = 5x = 5(3) = 15 years.

Question 16

Esha is currently 8 years older than Faisal. In 4 years, Esha's age will be 1.5 times Faisal's age. What will be the ratio of their ages 12 years from now?

Accepted Answer

Step 1: Let Faisal's current age = F. Then Esha's current age = F + 8. Step 2: In 4 years, Esha's age = F + 8 + 4 = F + 12 and Faisal's age = F + 4. Step 3: According to the condition, F + 12 = 1.5(F + 4) → F + 12 = 1.5F + 6 → 6 = 0.5F → F = 12. Step 4: Faisal's current age = 12 years and Esha's current age = 12 + 8 = 20 years. Step 5: In 12 years, Faisal's age = 12 + 12 = 24 years and Esha's age = 20 + 12 = 32 years. Step 6: Ratio = 32:24 = 4:3.

Question 17

The present ages of Chitra and Deepak are in the ratio 7:5. Six years ago, their ages were in the ratio 5:3. After how many years will their ages be in the ratio 9:7?

Accepted Answer

Step 1: Let Chitra's present age = 7x and Deepak's present age = 5x. Step 2: Six years ago, Chitra's age = 7x - 6 and Deepak's age = 5x - 6. Step 3: According to the condition, (7x - 6)/(5x - 6) = 5/3. Step 4: Cross multiply: 3(7x - 6) = 5(5x - 6) → 21x - 18 = 25x - 30 → 12 = 4x → x = 3. Step 5: Chitra's present age = 7(3) = 21 years and Deepak's present age = 5(3) = 15 years. Step 6: Let after y years, their ages be in ratio 9:7. Then (21 + y)/(15 + y) = 9/7. Step 7: Cross multiply: 7(21 + y) = 9(15 + y) → 147 + 7y = 135 + 9y → 12 = 2y → y = 6 years.

Question 18

Five years ago, the ratio of Priya's age to Quincy's age was 3:5. If Quincy is currently 30 years old, what will be the ratio of their ages 10 years from now?

Accepted Answer

Step 1: Quincy's current age = 30 years. Step 2: Five years ago, Quincy's age = 30 - 5 = 25 years. Step 3: Five years ago, the ratio was 3:5, so Priya's age five years ago = (3/5) × 25 = 15 years. Step 4: Priya's current age = 15 + 5 = 20 years. Step 5: Ten years from now, Priya's age = 20 + 10 = 30 years and Quincy's age = 30 + 10 = 40 years. Step 6: Ratio = 30:40 = 3:4.

Question 19

Divya is currently 4 times as old as Esha. In 6 years, Divya will be 2.5 times as old as Esha. What is the difference between their present ages?

Accepted Answer

Step 1: Let Esha's present age = y and Divya's present age = 4y. Step 2: After 6 years, Esha's age = y + 6 and Divya's age = 4y + 6. Step 3: Given that 4y + 6 = 2.5(y + 6). Step 4: 4y + 6 = 2.5y + 15. Step 5: 4y - 2.5y = 15 - 6. Step 6: 1.5y = 9. Step 7: y = 6. Step 8: Esha's present age = 6 years and Divya's present age = 4(6) = 24 years. Step 9: Difference = 24 - 6 = 18 years.

Question 20

The ratio of the present ages of Arun and Bhavna is 4:5. Five years ago, the ratio of their ages was 3:4. After how many years will the ratio of their ages be 6:7?

Accepted Answer

Step 1: Let present ages be Arun = 4x and Bhavna = 5x. Step 2: Five years ago, ages were (4x - 5) and (5x - 5), with ratio 3:4. So, (4x - 5)/(5x - 5) = 3/4. Cross-multiply: 4(4x - 5) = 3(5x - 5) → 16x - 20 = 15x - 15 → x = 5. Step 3: Present ages are Arun = 20 and Bhavna = 25. Step 4: Let after y years, ratio is 6:7. Then (20 + y)/(25 + y) = 6/7. Cross-multiply: 7(20 + y) = 6(25 + y) → 140 + 7y = 150 + 6y → y = 10. Therefore, the answer is 10 years.

Question 21

The ratio of ages of Ravi and Sita is 4:5. The ratio of ages of Sita and Tina is 3:2. If Ravi is 24 years old, what is Tina's age?

Accepted Answer

Step 1: Ravi:Sita = 4:5 and Ravi = 24. Step 2: From the ratio, 4 parts = 24, so 1 part = 6 years. Step 3: Sita's age = 5 parts = 5 × 6 = 30 years. Step 4: Sita:Tina = 3:2 and Sita = 30. Step 5: From this ratio, 3 parts = 30, so 1 part = 10 years. Step 6: Tina's age = 2 parts = 2 × 10 = 20 years.

Question 22

The ratio of ages of A, B, and C is 2:3:4. If B is 9 years younger than C, then what will be the ratio of their ages after 5 years?

Accepted Answer

Step 1: Let ages be A = 2x, B = 3x, C = 4x. Step 2: From the condition 'B is 9 years younger than C': C - B = 9 → 4x - 3x = 9 → x = 9. Step 3: Current ages: A = 18, B = 27, C = 36. Step 4: After 5 years: A = 23, B = 32, C = 41. Step 5: Ratio after 5 years = 23:32:41. Step 6: Check if this simplifies: GCD(23, 32, 41) = 1 (all are coprime). Therefore, answer is 23:32:41.

Question 23

The ratio of ages of A and B is 5:3. Four years ago, the ratio of their ages was 7:4. After how many years will the ratio of their ages be 9:7?

Accepted Answer

Step 1: Let current ages be A = 5x and B = 3x. Step 2: Four years ago: (5x - 4):(3x - 4) = 7:4. Step 3: Cross multiply: 4(5x - 4) = 7(3x - 4) → 20x - 16 = 21x - 28 → x = 12. Step 4: Current ages: A = 60, B = 36. Step 5: After n years: (60 + n):(36 + n) = 9:7. Step 6: 7(60 + n) = 9(36 + n) → 420 + 7n = 324 + 9n → 96 = 2n → n = 48. Therefore, answer is 48 years.

Question 24

A father is 3 times as old as his son. If the father's age 5 years ago was equal to 4 times his son's age 5 years ago, then what was the father's age 10 years ago?

Accepted Answer

Step 1: Let son's current age = s, father's current age = f. Step 2: From first condition: f = 3s. Step 3: From second condition: (f - 5) = 4(s - 5). Step 4: Substitute f = 3s into the second equation: 3s - 5 = 4s - 20. Step 5: Solve: 3s - 4s = -20 + 5 → -s = -15 → s = 15. Step 6: Father's current age: f = 3 × 15 = 45. Step 7: Father's age 10 years ago = 45 - 10 = 35. Therefore, answer is 35 years.

Question 25

The ratio of the present ages of Arun and Bhavna is 4:5. Five years ago, the ratio of their ages was 3:4. After how many years from now will the ratio of their ages be 6:7?

Accepted Answer

Step 1: Let present ages be Arun = 4x and Bhavna = 5x. Step 2: Five years ago, ratio was (4x - 5):(5x - 5) = 3:4. Step 3: Cross-multiply: 4(4x - 5) = 3(5x - 5) → 16x - 20 = 15x - 15 → x = 5. Step 4: Present ages: Arun = 20, Bhavna = 25. Step 5: After n years, ratio is (20 + n):(25 + n) = 6:7. Step 6: Cross-multiply: 7(20 + n) = 6(25 + n) → 140 + 7n = 150 + 6n → n = 10. Therefore, the answer is 10 years.

Question 26

The present ages of three persons P, Q, and R are in the ratio 4:5:6. If the sum of their ages 8 years ago was 66 years, what will be the sum of their ages after 12 years?

Accepted Answer

Step 1: Let current ages be P = 4x, Q = 5x, R = 6x. Step 2: Eight years ago, their ages were (4x - 8), (5x - 8), (6x - 8). Step 3: Sum 8 years ago: (4x - 8) + (5x - 8) + (6x - 8) = 66. Step 4: Simplify: 15x - 24 = 66 → 15x = 90 → x = 6. Step 5: Current ages: P = 24, Q = 30, R = 36. Step 6: Sum of current ages = 24 + 30 + 36 = 90. Step 7: After 12 years, sum = 90 + (3 × 12) = 90 + 36 = 126. Therefore, answer is 126 years.

Question 27

The ratio of the present ages of Arun and Bhavna is 4:5. Five years ago, the ratio of their ages was 3:4. After how many years from now will the ratio of their ages be 6:7?

Accepted Answer

Step 1: Let present ages be Arun = 4x and Bhavna = 5x. Step 2: Five years ago, Arun's age was 4x - 5 and Bhavna's age was 5x - 5. Step 3: Given (4x - 5):(5x - 5) = 3:4, so 4(4x - 5) = 3(5x - 5). Step 4: 16x - 20 = 15x - 15, therefore x = 5. Step 5: Present ages: Arun = 20 years, Bhavna = 25 years. Step 6: Let after y years, ratio becomes 6:7. Step 7: (20 + y):(25 + y) = 6:7, so 7(20 + y) = 6(25 + y). Step 8: 140 + 7y = 150 + 6y, therefore y = 10. The answer is 10 years.

Question 28

The ratio of the ages of Mohan and Sohan is 4:5. If the sum of their ages is 36 years, what is Mohan's age?

Accepted Answer

Step 1: Let Mohan's age = 4x and Sohan's age = 5x (from ratio 4:5). Step 2: Sum of their ages = 4x + 5x = 36. Step 3: 9x = 36, therefore x = 4. Step 4: Mohan's age = 4x = 4(4) = 16 years.

Question 29

The ratio of the present ages of Arun and Bhavna is 5:3. If Arun is 20 years older than Bhavna, what is Bhavna's present age?

Accepted Answer

Step 1: Let Arun's age = 5x and Bhavna's age = 3x (from ratio 5:3). Step 2: Given that Arun is 20 years older than Bhavna, so 5x - 3x = 20. Step 3: 2x = 20, therefore x = 10. Step 4: Bhavna's age = 3x = 3(10) = 30 years.

Question 30

The present ages of Ravi and Kavi are in the ratio 3:2. Six years hence, their ages will be in the ratio 5:4. What will be Ravi's age after 10 years?

Accepted Answer

Step 1: Let Ravi's current age = 3x and Kavi's current age = 2x. Step 2: After 6 years, Ravi's age = 3x + 6 and Kavi's age = 2x + 6. Step 3: Given that after 6 years, the ratio is 5:4, so (3x + 6):(2x + 6) = 5:4. Step 4: Cross-multiply: 4(3x + 6) = 5(2x + 6). Step 5: 12x + 24 = 10x + 30. Step 6: 2x = 6, so x = 3. Step 7: Ravi's current age = 3x = 3(3) = 9 years. Step 8: Ravi's age after 10 years = 9 + 10 = 19 years.

Question 31

The ratio of ages of Mohan and Sohan is 7:5. After 4 years, their ages will be in the ratio 9:7. What is Mohan's current age?

Accepted Answer

Step 1: Let Mohan's current age = 7x and Sohan's current age = 5x. Step 2: After 4 years, Mohan's age = 7x + 4 and Sohan's age = 5x + 4. Step 3: Given that after 4 years, the ratio is 9:7, so (7x + 4):(5x + 4) = 9:7. Step 4: Cross-multiply: 7(7x + 4) = 9(5x + 4). Step 5: 49x + 28 = 45x + 36. Step 6: 4x = 8, so x = 2. Step 7: Mohan's current age = 7x = 7(2) = 14 years.

Question 32

Five years ago, the ratio of Priya's age to Deepak's age was 4:5. If Deepak is currently 30 years old, what is Priya's current age?

Accepted Answer

Step 1: Deepak's current age = 30 years. Step 2: Five years ago, Deepak's age = 30 - 5 = 25 years. Step 3: Five years ago, the ratio was 4:5, so Priya's age five years ago : Deepak's age five years ago = 4:5. Step 4: Let Priya's age five years ago = 4y, then 4y : 25 = 4:5. Step 5: 4y/25 = 4/5, so 4y = 20, therefore y = 5. Step 6: Priya's age five years ago = 4(5) = 20 years. Step 7: Priya's current age = 20 + 5 = 25 years.

Question 33

The ratio of Ravi's age to Rani's age is 3:2. After 8 years, their ages will be in the ratio 5:4. What is Ravi's current age?

Accepted Answer

Step 1: Let Ravi's current age = 3x and Rani's current age = 2x. Step 2: After 8 years, Ravi's age = 3x + 8 and Rani's age = 2x + 8. Step 3: After 8 years, the ratio is 5:4, so (3x + 8)/(2x + 8) = 5/4. Step 4: Cross multiply: 4(3x + 8) = 5(2x + 8). Step 5: 12x + 32 = 10x + 40. Step 6: 2x = 8, therefore x = 4. Step 7: Ravi's current age = 3x = 3(4) = 12 years.

Question 34

The ratio of ages of Amit and Bunty is 3:5. If Amit is 18 years old, what is the age of Bunty?

Accepted Answer

Step 1: Let Amit's age = 3x and Bunty's age = 5x. Step 2: Given 3x = 18, so x = 6. Step 3: Bunty's age = 5x = 5 × 6 = 30 years. Therefore, the answer is 30 years.

Question 35

Chitra's age is 2/3 of Deepak's age. If the sum of their ages is 60 years, what will be Chitra's age after 6 years?

Accepted Answer

Step 1: Let Deepak's age = d and Chitra's age = (2/3)d. Step 2: Sum of ages: (2/3)d + d = 60. Step 3: Combine: (2d + 3d)/3 = 60 → 5d/3 = 60. Step 4: Solve: 5d = 180 → d = 36. Step 5: Deepak's age = 36 years and Chitra's age = (2/3)(36) = 24 years. Step 6: Chitra's age after 6 years = 24 + 6 = 30 years.

Question 36

The ratio of ages of Ravi and Sita is 7:6. If Ravi is 7 years older than Sita, what will be the ratio of their ages after 14 years?

Accepted Answer

Step 1: Let Ravi's age = 7k and Sita's age = 6k. Step 2: Given that Ravi is 7 years older: 7k - 6k = 7 → k = 7. Step 3: Ravi's present age = 7(7) = 49 years and Sita's present age = 6(7) = 42 years. Step 4: After 14 years, Ravi's age = 49 + 14 = 63 years and Sita's age = 42 + 14 = 56 years. Step 5: Ratio after 14 years = 63:56 = 9:8 (dividing both by 7).

Question 37

Five years ago, the ratio of Priya's age to Quincy's age was 3:4. Five years hence, the ratio will be 4:5. What will be Quincy's age after 10 years from now?

Accepted Answer

Step 1: Let Priya's age 5 years ago = 3y and Quincy's age 5 years ago = 4y. Step 2: Priya's present age = 3y + 5 and Quincy's present age = 4y + 5. Step 3: After 5 years, Priya's age = 3y + 10 and Quincy's age = 4y + 10. Step 4: Set up equation: (3y + 10)/(4y + 10) = 4/5. Step 5: Cross multiply: 5(3y + 10) = 4(4y + 10) → 15y + 50 = 16y + 40 → y = 10. Step 6: Quincy's present age = 4(10) + 5 = 45 years. Step 7: Quincy's age after 10 years = 45 + 10 = 55 years.

Question 38

The present age of Aman is 3 times the present age of Bimal. After 12 years, Aman's age will be twice Bimal's age. What is the difference between their present ages?

Accepted Answer

Step 1: Let Bimal's present age = b and Aman's present age = 3b. Step 2: After 12 years, Aman's age = 3b + 12 and Bimal's age = b + 12. Step 3: Given condition: 3b + 12 = 2(b + 12). Step 4: Expand: 3b + 12 = 2b + 24. Step 5: Solve: 3b - 2b = 24 - 12 → b = 12. Step 6: Bimal's present age = 12 years and Aman's present age = 3(12) = 36 years. Step 7: Difference = 36 - 12 = 24 years.

Question 39

The ratio of ages of Meera and Nisha is 5:7. If Meera is 10 years younger than Nisha, what will be the ratio of their ages after 5 years?

Accepted Answer

Step 1: Let Meera's age = 5k and Nisha's age = 7k. Step 2: Given that Meera is 10 years younger: 7k - 5k = 10 → 2k = 10 → k = 5. Step 3: Meera's present age = 5(5) = 25 years and Nisha's present age = 7(5) = 35 years. Step 4: After 5 years, Meera's age = 25 + 5 = 30 years and Nisha's age = 35 + 5 = 40 years. Step 5: Ratio after 5 years = 30:40 = 3:4.

Question 40

The ages of three persons A, B, and C are in the ratio 2:3:4. If the sum of their ages is 54 years, and after how many years will the ratio of their ages be 3:4:5?

Accepted Answer

Step 1: Let ages be A = 2x, B = 3x, C = 4x. Step 2: Sum: 2x + 3x + 4x = 54 → 9x = 54 → x = 6. Step 3: Current ages: A = 12, B = 18, C = 24. Step 4: After n years: A = 12 + n, B = 18 + n, C = 24 + n. Step 5: Ratio condition: (12 + n):(18 + n):(24 + n) = 3:4:5. Step 6: From first two terms: 4(12 + n) = 3(18 + n) → 48 + 4n = 54 + 3n → n = 6. Step 7: Verify with last two terms: 5(18 + 6) = 4(24 + 6) → 5(24) = 4(30) → 120 = 120 ✓.

Question 41

The present age of Aman is 40% more than Bimal's present age. Five years ago, Aman's age was 50% more than Bimal's age at that time. After how many years will Aman's age be 25% more than Bimal's age?

Accepted Answer

Step 1: Let Bimal's present age = B. Then Aman's present age = 1.4B. Step 2: Five years ago: Aman = 1.4B-5, Bimal = B-5. Step 3: Condition: 1.4B-5 = 1.5(B-5) → 1.4B-5 = 1.5B-7.5 → -0.1B = -2.5 → B = 25. Step 4: Aman's present age = 1.4×25 = 35. Step 5: After y years, Aman = 35+y, Bimal = 25+y. Step 6: Condition: 35+y = 1.25(25+y) → 35+y = 31.25+1.25y → 3.75 = 0.25y → y = 15. Therefore, answer is 15 years.

Question 42

The ratio of ages of A and B five years ago was 5:4. The ratio of their ages five years hence will be 7:6. What is the sum of their current ages?

Accepted Answer

Step 1: Let ages 5 years ago be A = 5x, B = 4x. Step 2: Current ages: A = 5x + 5, B = 4x + 5. Step 3: Ages 5 years hence: A = 5x + 10, B = 4x + 10. Step 4: Future ratio condition: (5x + 10):(4x + 10) = 7:6. Step 5: Cross multiply: 6(5x + 10) = 7(4x + 10) → 30x + 60 = 28x + 70 → 2x = 10 → x = 5. Step 6: Current ages: A = 5(5) + 5 = 30, B = 4(5) + 5 = 25. Step 7: Sum = 30 + 25 = 55.

Question 43

The ratio of the present ages of Arun and Bhavna is 4:5. Four years ago, the ratio of their ages was 3:4. After how many years from now will the ratio of their ages be 6:7?

Accepted Answer

Step 1: Let present ages be Arun = 4x and Bhavna = 5x. Step 2: Four years ago, ratio was (4x-4):(5x-4) = 3:4. Step 3: Cross multiply: 4(4x-4) = 3(5x-4) → 16x-16 = 15x-12 → x = 4. Step 4: Present ages: Arun = 16, Bhavna = 20. Step 5: After y years, (16+y):(20+y) = 6:7. Step 6: 7(16+y) = 6(20+y) → 112+7y = 120+6y → y = 8. Therefore, answer is 8 years.

Question 44

A father's age is 3 times his son's age. After 15 years, the father's age will be twice the son's age. If the father's current age is F and son's current age is S, what is the ratio F:S after 20 years?

Accepted Answer

Step 1: Current condition: F = 3S. Step 2: Future condition (after 15 years): F + 15 = 2(S + 15). Step 3: Substitute F = 3S: 3S + 15 = 2S + 30 → S = 15. Step 4: F = 3 × 15 = 45. Step 5: After 20 years: F = 65, S = 35. Step 6: Ratio = 65:35 = 13:7.

Question 45

The ratio of ages of A and B is 7:5. Four years ago, the ratio of their ages was 3:2. After how many years will the ratio of their ages be 9:7?

Accepted Answer

Step 1: Let current ages be A = 7x and B = 5x. Step 2: Four years ago: (7x - 4):(5x - 4) = 3:2. Step 3: Cross multiply: 2(7x - 4) = 3(5x - 4) → 14x - 8 = 15x - 12 → x = 4. Step 4: Current ages: A = 28, B = 20. Step 5: After n years: (28 + n):(20 + n) = 9:7. Step 6: 7(28 + n) = 9(20 + n) → 196 + 7n = 180 + 9n → 16 = 2n → n = 8.

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