**Age Problems**

**Question 1:**

**The sum of the present ages of A and B is 64. Five years ago, the ratio of their ages was 3:2. Find their present ages.**

**Solution:**

**Let the present age of A be 3x and B be 2x.**

**According to the given information, 3x + 2x = 64.**

**Simplifying the equation, 5x = 64.**

**Dividing both sides by 5, we get x = 12.8.**

**Therefore, the present age of A = 3x = 3 * 12.8 = 38.4 years.**

**And the present age of B = 2x = 2 * 12.8 = 25.6 years.**

**Requested by: Ahmed**

**Question 2:**

**The sum of the present ages of a father and his son is 48 years. Four years ago, the father’s age was five times the age of the son. Find their present ages.**

**Solution:**

**Let the present age of the son be x. Therefore, the present age of the father is 48 – x.**

**According to the given information, 48 – x – 4 = 5(x – 4).**

**Simplifying the equation, 48 – x – 4 = 5x – 20.**

**Combining like terms, 44 – x = 5x – 20.**

**Bringing like terms to one side, 6x = 64.**

**Dividing both sides by 6, we get x = 10.67.**

**Therefore, the present age of the son is approximately 10.67 years.**

**And the present age of the father is approximately 48 – 10.67 = 37.33 years.**

**Requested by: Ahmed**

**Question 3:**

**The average age of a family of 5 members is 24 years. If the youngest member is 8 years old, what is the average age of the family excluding the youngest member?**

**Solution:**

**The sum of the ages of the family members is 24 * 5 = 120 years.**

**Since the youngest member is 8 years old, the sum of the ages of the remaining 4 members is 120 – 8 = 112 years.**

**Therefore, the average age of the family excluding the youngest member is 112/4 = 28 years.**

**Requested by: Inaam**

**Question 4:**

**The present age of a father is four times the age of his son. The difference between their ages is 20 years. Find their present ages.**

**Solution:**

**Let the present age of the son be x. Therefore, the present age of the father is 4x.**

**According to the given information, 4x – x = 20.**

**Simplifying the equation, 3x = 20.**

**Dividing both sides by 3, we get x = 6.67.**

**Therefore, the present age of the son is approximately 6.67 years.**

**And the present age of the father is approximately 4 * 6.67 = 26.67 years.**

**Requested by: Faisal**

**Question 5:**

**The ratio of the present ages of A and B is 5:3. If the difference between their ages is 8 years, find their present ages.**

**Solution:**

**Let the present age of A be 5x and B be 3x.**

**According to the given information, 5x – 3x = 8.**

**Simplifying the equation, 2x = 8.**

**Dividing both sides by 2, we get x = 4.**

**Therefore, the present age of A = 5x = 5 * 4 = 20 years.**

**And the present age of B = 3x = 3 * 4 = 12 years.**

**Requested by: Faisal**

**Question 6:**

**The average age of a group of 8 friends is 32 years. If the age of one of the friends is 40 years, what is the average age of the remaining friends?**

**Solution:**

**The sum of the ages of the 8 friends is 32 * 8 = 256 years.**

**Since one of the friends is 40 years old, the sum of the ages of the remaining 7 friends is 256 – 40 = 216 years.**

**Therefore, the average age of the remaining friends is 216/7 ≈ 30.86 years.**

**Requested by: Zohaib**

**Question 7:**

**The age of a man is three times the age of his son. After 15 years, the man’s age will be twice that of his son. Find their present ages.**

**Solution:**

**Let the present age of the son be x. Therefore, the present age of the man is 3x.**

**After 15 years, the son’s age will be x + 15, and the man’s age will be 3x + 15.**

**According to the given information, 3x + 15 = 2(x + 15).**

**Simplifying the equation, 3x + 15 = 2x + 30.**

**Bringing like terms to one side, x = 15.**

**Therefore, the present age of the son is 15 years.**

**And the present age of the man is 3 * 15 = 45 years.**

**Requested by: Samad**

**Question 8:**

**The sum of the ages of a mother and her daughter is 50 years. Five years ago, the mother was seven times as old as the daughter. Find their present ages.**

**Solution:**

**Let the present age of the daughter be x. Therefore, the present age of the mother is 50 – x.**

**According to the given information, 50 – x – 5 = 7(x – 5).**

**Simplifying the equation, 45 – x = 7x – 35.**

**Bringing like terms to one side, 8x = 80.**

**Dividing both sides by 8, we get x = 10.**

**Therefore, the present age of the daughter is 10 years.**

**And the present age of the mother is 50 – 10 = 40 years.**

**Requested by: Sarang**

**Question 9:**

**The average age of a group of 10 friends is 25 years. If the age of one of the friends is 18 years, what is the average age of the remaining friends?**

**Solution:**

**The sum of the ages of the 10 friends is 25 * 10 = 250 years.**

**Since one of the friends is 18 years old, the sum of the ages of the remaining 9 friends is 250 – 18 = 232 years.**

**Therefore, the average age of the remaining friends is 232/9 ≈ 25.78 years.**

**Requested by: Ali**

**Question 10:**

**The sum of the present ages of a father and his son is 72 years. Ten years ago, the father’s age was five times the age of the son. Find their present ages.**

**Solution:**

**Let the present age of the son be x. Therefore, the present age of the father is 72 – x.**

**According to the given information, 72 – x – 10 = 5(x – 10).**

**Simplifying the equation, 62 – x = 5x – 50.**

**Bringing like terms to one side, 6x = 112.**

**Dividing both sides by 6, we get x = 18.67.**

**Therefore, the present age of the son is approximately 18.67 years.**

**And the present age of the father is approximately 72 – 18.67 = 53.33 years.**

**Requested by: Aakash**

**Question 11:**

**The ratio of the present ages of A and B is 7:5. If the difference between their ages is 12 years, find their present ages.**

**Solution:**

**Let the present age of A be 7x and B be 5x.**

**According to the given information, 7x – 5x = 12.**

**Simplifying the equation, 2x = 12.**

**Dividing both sides by 2, we get x = 6.**

**Therefore, the present age of A = 7x = 7 * 6 = 42 years.**

**And the present age of B = 5x = 5 * 6 = 30 years.**

**Requested by: Anwar**

**Question 12:**

**The average age of a group of 12 friends is 28 years. If the age of one of the friends is 30 years, what is the average age of the remaining friends?**

**Solution:**

**The sum of the ages of the 12 friends is 28 * 12 = 336 years.**

**Since one of the friends is 30 years old, the sum of the ages of the remaining 11 friends is 336 – 30 = 306 years.**

**Therefore, the average age of the remaining friends is 306/11 ≈ 27.82 years.**

**Requested by: Zulfiqar**

**Question 13:**

**The age of a man is four times the age of his daughter. After 10 years, the man’s age will be three times that of his daughter. Find their present ages.**

**Solution:**

**Let the present age of the daughter be x. Therefore, the present age of the man is 4x.**

**After 10 years, the daughter’s age will be x + 10, and the man’s age will be 4x + 10.**

**According to the given information, 4x + 10 = 3(x + 10).**

**Simplifying the equation, 4x + 10 = 3x + 30.**

**Bringing like terms to one side, x = 20.**

**Therefore, the present age of the daughter is 20 years.**

**And the present age of the man is 4 * 20 = 80 years.**

**Requested by: Asim**

**Question 14:**

**The sum of the ages of a mother and her daughter is 60 years. Five years ago, the mother was four times as old as the daughter. Find their present ages.**

**Solution:**

**Let the present age of the daughter be x. Therefore, the present age of the mother is 60 – x.**

**According to the given information, 60 – x – 5 = 4(x – 5).**

**Simplifying the equation, 55 – x = 4x – 20.**

**Bringing like terms to one side, 5x = 75.**

**Dividing both sides by 5, we get x = 15.**

**Therefore, the present age of the daughter is 15 years.**

**And the present age of the mother is 60 – 15 = 45 years.**

**Requested by: Azhar**

**Question 15:**

**The average age of a group of 15 friends is 35 years. If the age of one of the friends is 42 years, what is the average age of the remaining friends?**

**Solution:**

**The sum of the ages of the 15 friends is 35 * 15 = 525 years.**

**Since one of the friends is 42 years old, the sum of the ages of the remaining 14 friends is 525 – 42 = 483 years.**

**Therefore, the average age of the remaining friends is 483/14 ≈ 34.5 years.**

**Requested by: Mazhar**

**Question 16:**

**The ratio of the present ages of A and B is 2:3. After 10 years, the ratio of their ages will be 3:4. Find their present ages.**

**Solution:**

**Let the present age of A be 2x and B be 3x.**

**After 10 years, the ages of A and B will be 2x + 10 and 3x + 10, respectively.**

**According to the given information, (2x + 10)/(3x + 10) = 3/4.**

**Cross-multiplying, we get 8x + 40 = 9x + 30.**

**Bringing like terms to one side, x = 10.**

**Therefore, the present age of A = 2x = 2 * 10 = 20 years.**

**And the present age of B = 3x = 3 * 10 = 30 years.**

**Requested by: Faiz**

**Question 17:**

**The average age of a group of 20 friends is 40 years. If the age of one of the friends is 50 years, what is the average age of the remaining friends?**

**Solution:**

**The sum of the ages of the 20 friends is 40 * 20 = 800 years.**

**Since one of the friends is 50 years old, the sum of the ages of the remaining 19 friends is 800 – 50 = 750 years.**

**Therefore, the average age of the remaining friends is 750/19 ≈ 39.47 years.**

**Requested by: Sahil**

**Question 18:**

**The present age of a father is three times the age of his son. The sum of their ages is 48 years. Find their present ages.**

**Solution:**

**Let the present age of the son be x. Therefore, the present age of the father is 3x.**

**According to the given information, x + 3x = 48.**

**Simplifying the equation, 4x = 48.**

**Dividing both sides by 4, we get x = 12.**

**Therefore, the present age of the son is 12 years.**

**And the present age of the father is 3 * 12 = 36 years.**

**Requested by: Zubair**

**Question 19:**

**The sum of the ages of a mother and her daughter is 36 years. Four years ago, the mother was five times as old as the daughter. Find their present ages.**

**Solution:**

**Let the present age of the daughter be x. Therefore, the present age of the mother is 36 – x.**

**According to the given information, 36 – x – 4 = 5(x – 4).**

**Simplifying the equation, 32 – x = 5x – 20.**

**Bringing like terms to one side, 6x = 52.**

**Dividing both sides by 6, we get x = 8.67.**

**Therefore, the present age of the daughter is approximately 8.67 years.**

**And the present age of the mother is 36 – 8.67 = 27.33 years.**

**Requested by: Mazhar**

**Question 20:**

**The average age of a group of 25 friends is 30 years. If the age of one of the friends is 35 years, what is the average age of the remaining friends?**

**Solution:**

**The sum of the ages of the 25 friends is 30 * 25 = 750 years.**

**Since one of the friends is 35 years old, the sum of the ages of the remaining 24 friends is 750 – 35 = 715 years.**

**Therefore, the average age of the remaining friends is 715/24 ≈ 29.79 years.**

**Requested by: Faizan**

**Question 21:**

**The present ages of John and Mary are in the ratio of 5:3. If the sum of their ages is 64 years, what are their present ages?**

**Solution:**

**Let the present age of John be 5x and Mary be 3x.**

**According to the given information, 5x + 3x = 64.**

**Simplifying the equation, 8x = 64.**

**Dividing both sides by 8, we get x = 8.**

**Therefore, the present age of John is 5x = 5 * 8 = 40 years.**

**And the present age of Mary is 3x = 3 * 8 = 24 years.**

**Requested by: Azaan**

**Question 22:**

**The average age of a family of 6 members is 35 years. If the average age of the parents is 40 years, what is the average age of the children?**

**Solution:**

**The sum of the ages of the parents is 40 * 2 = 80 years.**

**The sum of the ages of the children is the sum of the ages of all family members minus the sum of the ages of the parents.**

**Therefore, the sum of the ages of the children is (35 * 6) – 80 = 210 – 80 = 130 years.**

**Since there are 4 children, the average age of the children is 130/4 = 32.5 years.**

**Requested by: Azaan**

**Question 23:**

**The sum of the ages of a father and his son is 48 years. Four years ago, the father’s age was three times the age of the son. Find their present ages.**

**Solution:**

**Let the present age of the son be x. Therefore, the present age of the father is 48 – x.**

**According to the given information, 48 – x – 4 = 3(x – 4).**

**Simplifying the equation, 44 – x = 3x – 12.**

**Bringing like terms to one side, 4x = 56.**

**Dividing both sides by 4, we get x = 14.**

**Therefore, the present age of the son is 14 years.**

**And the present age of the father is 48 – 14 = 34 years.**

**Requested by: Mustafa**

**Question 24:**

**The ratio of the present ages of A and B is 3:5. After 10 years, the ratio of their ages will be 4:7. Find their present ages.**

**Solution:**

**Let the present age of A be 3x and B be 5x.**

**After 10 years, the ages of A and B will be 3x + 10 and 5x + 10, respectively.**

**According to the given information, (3x + 10)/(5x + 10) = 4/7.**

**Cross-multiplying, we get 21x + 70 = 20x + 40.**

**Bringing like terms to one side, x = -30.**

**Since the age cannot be negative, this is an invalid solution.**

**Therefore, there is no valid solution for this problem.**

**Requested by: Mustafa**

**Question 25:**

**The average age of a group of 15 friends is 30 years. If the age of one of the friends is 35 years, what is the average age of the remaining friends?**

**Solution:**

**The sum of the ages of the 15 friends is 30 * 15 = 450 years.**

**Since one of the friends is 35 years old, the sum of the ages of the remaining 14 friends is 450 – 35 = 415 years.**

**Therefore, the average age of the remaining friends is 415/14 ≈ 29.64 years.**

**Requested by: Kabeer**

**Question 26:**

**The age of a man is four times the age of his son. Five years ago, the man’s age was three times the age of the son. Find their present ages.**

**Solution:**

**Let the present age of the son be x. Therefore, the present age of the man is 4x.**

**Five years ago, the son’s age was x – 5, and the man’s age was 4x – 5.**

**According to the given information, 4x – 5 = 3(x – 5).**

**Simplifying the equation, 4x – 5 = 3x – 15.**

**Bringing like terms to one side, x = 10.**

**Therefore, the present age of the son is 10 years.**

**And the present age of the man is 4 * 10 = 40 years.**

**Requested by: Ali**

**Question 27:**

**The sum of the ages of a brother and sister is 40 years. Four years ago, the brother’s age was twice the age of the sister. Find their present ages.**

**Solution:**

**Let the present age of the sister be x. Therefore, the present age of the brother is 40 – x.**

**Four years ago, the sister’s age was x – 4, and the brother’s age was 40 – x – 4.**

**According to the given information, 40 – x – 4 = 2(x – 4).**

**Simplifying the equation, 36 – x = 2x – 8.**

**Bringing like terms to one side, 3x = 44.**

**Dividing both sides by 3, we get x = 14.67.**

**Therefore, the present age of the sister is approximately 14.67 years.**

**And the present age of the brother is 40 – 14.67 = 25.33 years.**

**Requested by: Ilyas**

**Question 28:**

**The average age of a group of 20 friends is 35 years. If the age of one of the friends is 40 years, what is the average age of the remaining friends?**

**Solution:**

**The sum of the ages of the 20 friends is 35 * 20 = 700 years.**

**Since one of the friends is 40 years old, the sum of the ages of the remaining 19 friends is 700 – 40 = 660 years.**

**Therefore, the average age of the remaining friends is 660/19 ≈ 34.74 years.**

**Requested by: Ilyas**

**Question 29:**

**The present ages of two friends are in the ratio of 2:3. Four years ago, the ratio of their ages was 1:2. Find their present ages.**

**Solution:**

**Let the present age of the first friend be 2x and the second friend be 3x.**

**Four years ago, the ages of the friends were 2x – 4 and 3x – 4.**

**According to the given information, (2x – 4)/(3x – 4) = 1/2.**

**Cross-multiplying, we get 4x – 8 = 3x – 4.**

**Bringing like terms to one side, x = 4.**

**Therefore, the present age of the first friend is 2x = 2 * 4 = 8 years.**

**And the present age of the second friend is 3x = 3 * 4 = 12 years.**

**Requested by: Azlan**

**Question 30:**

**The average age of a group of 30 friends is 25 years. If the age of one of the friends is 30 years, what is the average age of the remaining friends?**

**Solution:**

**The sum of the ages of the 30 friends is 25 * 30 = 750 years.**

**Since one of the friends is 30 years old, the sum of the ages of the remaining 29 friends is 750 – 30 = 720 years.**

**Therefore, the average age of the remaining friends is 720/29 ≈ 24.83 years.**

**Requested by: Azlan**

**Question 31:**

**The ratio of the present ages of a father and his son is 5:2. Four years ago, the ratio of their ages was 11:4. Find their present ages.**

**Solution:**

**Let the present age of the father be 5x and the son be 2x.**

**Four years ago, the ages of the father and son were 5x – 4 and 2x – 4, respectively.**

**According to the given information, (5x – 4)/(2x – 4) = 11/4.**

**Cross-multiplying, we get 20x – 16 = 22x – 44.**

**Bringing like terms to one side, x = 14.**

**Therefore, the present age of the father is 5x = 5 * 14 = 70 years.**

**And the present age of the son is 2x = 2 * 14 = 28 years.**

**Requested by: Azlan**

**Question 32:**

**The average age of a group of 40 students is 18 years. If the age of one of the students is 20 years, what is the average age of the remaining students?**

**Solution:**

**The sum of the ages of the 40 students is 18 * 40 = 720 years.**

**Since one of the students is 20 years old, the sum of the ages of the remaining 39 students is 720 – 20 = 700 years.**

**Therefore, the average age of the remaining students is 700/39 ≈ 17.95 years.**

**Requested by: Zain**

**Question 33:**

**The sum of the ages of a grandfather and his grandson is 80 years. The grandfather is 4 times as old as the grandson. Find their ages.**

**Solution:**

**Let the present age of the grandson be x. Therefore, the present age of the grandfather is 4x.**

**According to the given information, x + 4x = 80.**

**Simplifying the equation, 5x = 80.**

**Dividing both sides by 5, we get x = 16.**

**Therefore, the present age of the grandson is 16 years.**

**And the present age of the grandfather is 4 * 16 = 64 years.**

**Requested by: Rehman**

**Question 34:**

**The ratio of the present ages of A and B is 3:7. Five years ago, the ratio of their ages was 2:5. Find their present ages.**

**Solution:**

**Let the present age of A be 3x and B be 7x.**

**Five years ago, the ages of A and B were 3x – 5 and 7x – 5, respectively.**

**According to the given information, (3x – 5)/(7x – 5) = 2/5.**

**Cross-multiplying, we get 15x – 25 = 14x – 10.**

**Bringing like terms to one side, x = 15.**

**Therefore, the present age of A is 3x = 3 * 15 = 45 years.**

**And the present age of B is 7x = 7 * 15 = 105 years.**

**Requested by: Zohaib**

**Question 35:**

**The average age of a group of 25 friends is 32 years. If the age of one of the friends is 40 years, what is the average age of the remaining friends?**

**Solution:**

**The sum of the ages of the 25 friends is 32 * 25 = 800 years.**

**Since one of the friends is 40 years old, the sum of the ages of the remaining 24 friends is 800 – 40 = 760 years.**

**Therefore, the average age of the remaining friends is 760/24 = 31.67 years.**

**Requested by: Akram**

**Question 36:**

**The age of a father is 4 times the age of his son. Four years later, the age of the father will be three times the age of the son. Find their present ages.**

**Solution:**

**Let the present age of the son be x. Therefore, the present age of the father is 4x.**

**Four years later, the ages of the father and son will be 4x + 4 and x + 4, respectively.**

**According to the given information, 4x + 4 = 3(x + 4).**

**Simplifying the equation, 4x + 4 = 3x + 12.**

**Bringing like terms to one side, x = 8.**

**Therefore, the present age of the son is 8 years.**

**And the present age of the father is 4 * 8 = 32 years.**

**Requested by: Aakash**

**Question 37:**

**The sum of the present ages of a husband and wife is 60 years. The husband is twice as old as the wife. Find their ages.**

**Solution:**

**Let the present age of the wife be x. Therefore, the present age of the husband is 2x.**

**According to the given information, x + 2x = 60.**

**Simplifying the equation, 3x = 60.**

**Dividing both sides by 3, we get x = 20.**

**Therefore, the present age of the wife is 20 years.**

**And the present age of the husband is 2 * 20 = 40 years.**

**Requested by: Zain**

**Question 38:**

**The average age of a group of 50 employees is 35 years. If the age of one of the employees is 45 years, what is the average age of the remaining employees?**

**Solution:**

**The sum of the ages of the 50 employees is 35 * 50 = 1750 years.**

**Since one of the employees is 45 years old, the sum of the ages of the remaining 49 employees is 1750 – 45 = 1705 years.**

**Therefore, the average age of the remaining employees is 1705/49 ≈ 34.80 years.**

**Requested by: Zohaib**

**Question 39:**

**The present ages of two friends are in the ratio of 4:7. Seven years ago, the ratio of their ages was 3:5. Find their present ages.**

**Solution:**

**Let the present age of the first friend be 4x and the second friend be 7x.**

**Seven years ago, the ages of the friends were 4x – 7 and 7x – 7, respectively.**

**According to the given information, (4x – 7)/(7x – 7) = 3/5.**

**Cross-multiplying, we get 20x – 35 = 21x – 21.**

**Bringing like terms to one side, x = 14.**

**Therefore, the present age of the first friend is 4x = 4 * 14 = 56 years.**

**And the present age of the second friend is 7x = 7 * 14 = 98 years.**

**Requested by: Faizan**

**Question 40:**

**The average age of a group of 60 students is 21 years. If the age of one of the students is 25 years, what is the average age of the remaining students?**

**Solution:**

**The sum of the ages of the 60 students is 21 * 60 = 1260 years.**

**Since one of the students is 25 years old, the sum of the ages of the remaining 59 students is 1260 – 25 = 1235 years.**

**Therefore, the average age of the remaining students is 1235/59 ≈ 20.93 years.**

**Requested by: Hasnain**