TYPES OF RATIOS:
10. PROBLEMS ON AGES
In solving the problems related to ages, we come across three situations.
1. Age some years ago 2. Present Age
3. Age some years hence Models:
1. If the age of A, t years ago, was n1 times the age of B and at present the age of A is n2 times that of B, then finding the present Age of A and the present Age of B.
2. If the present age of A is n1 times the present age of B. If t years hence, the age of A would be n2 times that of B, then finding the present Age of A the present Age of B.
3. If the age of A, t1 years ago, was n1 times the age of B and if t2 years hence A‟s age would be n2 times that of B, then finding the present Age of A and the present Age of B.
4. The sum of present ages of A and B is S years. If t years ago, the age of A was n times the age of B, then finding the present Age of A and the present Age of B.
5. The sum of present ages of A and B is S years. If t years hence, the age of A would be n times the age of B, then finding the present Age of A and the present Age of B.
6. If the ratio of the present ages of A and B is a : b and t years hence, it will be c : d, then finding the present Age of A and the present Age of B.
SOLVED EXAMPLES
1. The age of Mr. Bindra is 3 times the age of his son. If 10 years ago, his age was 8 times the age of his son, then at that time what would be the age of Mr. Bindra.
Sol: 10 years ago: present:
Son = x son = x+10
Mr. Bindra = 8x Mr. Bindra = 8x+10
3(x+10) = 8x+10 3x+30 = 8x+10 x = 4
Mr. Bindra = 8x4+10 = 42
2. The age of Mr. Sinha is 7 times the age of his daughter. After 15 years, the age of Mr.
Sinha is only twice the age of his daughter. Find the present age of Mr. Sinha‟s daughter.
Sol: Present: After 15 years:
Daughter = x Daughter = x+15
Mr. Sinha = 7x Mr. Sinha = 7x+15 7x+15 = 2(x+15)
7x+15 = 2x+30 x = 3
Mr. Sinha‟s daughter = 3 years
3. 12 years ago Lekha‟s father was 5 times older than her. After 12 years, the father will be 3 times older than her. Find the present age of Lekha.
Sol: 12 years ago: Present: After 12 years:
Lekha = x Lekha = x+12 Lekha = x+24
Father = 5x Father = 5x+12 Father = 5x+24
3(x+24) = 5x+24
3x+72 = 5x+24
x = 24 Lekha = 24+12 = 36
4. The sum of the ages of A and B is 36 years. 2 years back, the age of A is 4 times the age of B. Find the difference between the present ages of A and B.
Sol: 2 years back: Present:
B = x B = x+2
A = 4x A = 4x+2
x+2+4x+2 = 36 x = 6.4
A-B = 25.6 – 6.4 = 19.2
5. The sum of the ages of father and a son is 44 years. After 8 years, the age of the father will be 5 times that of son. Find their respective ages.
Sol: After 8 years: Present:
Son = x Son = x – 8
Father = 5x Father = 5x-8 x-8+5x-8 = 44 x = 10
Son = 10-8 = 2 Father = 50-8 = 42
6. The ratio of the present ages of father and son is 3 : 1. After 10 years, it will become 5 : 2. Find the present age of the son.
Sol: Present: After 10 years:
Son = x Son = x+10
Father = 3x Father = 3x+10 3x 10 5
x 10 2
6x+20 = 5x+50 x = 30
son = 30 years
7. 4 years ago Kalyani was thrice as old as Ramya. If the ratio of their present ages is 4 : 3 respectively. Find the difference between their ages.
Sol: Present: 4 years ago:
Kalyani = 4x Kalyani = 4x-4
Ramya = 3x Ramya = 3x-4
3(3x-4) = 4x-4 9x-12 = 4x-4 x = 1.6
Kalyani – Ramya = 1.6
Brainstorming
1. The ratio of P‟s and Q‟s ages is 5:7. If the difference between the present age of Q and the age of P six years hence is 2, then what is the total of present ages of P and Q?
1. 52 yrs 2. 48 yrs 3. 56 yrs 4. None
2. The ratio between the present ages of P and Q is 5:8. After 4 years, the ratio between their ages will be 2:3. What is Q‟s present age?
1. 36 yrs 2. 20 yrs 3. 24 yrs 4. None
3. The ratio of present ages of Ram and Shyam is 7:8, respectively. Four years hence this ratio becomes 9:10, respectively. What is Ram‟s present age in years?
1. 18 2. 14 2. 17 4. None
4. One year ago the ratio of Karan‟s and Ankit‟s ages was 6:7, respectively. Four years hence this ratio would become 7:8. How old is Ankit?
1. 35 yrs 2. 30 yrs 3. 31 yrs 4. None
5. The sum of the ages of A & B is 50 years and the ratio between their ages is 7:3 then the age of A is how many years?
1. 15 2. 35 3. 20 4. 25
6. The sum of the ages of P & Q is 72 years and the ratio between their ages is 2:7. Then the ratio between their ages 8 years ago is __________
1. 2:5 2. 5:2 3. 10:15 4. 1:6
7. The ratio between the present ages of A & B in 4:5 and the sum of their ages after 5 years is 100 years. What will be the ratio of their ages at that time?
1. 9:10 2. 10:9 3. 9:11 4. 11:9
8. The ratio between the ages of a father and his son, 10 years ago was 9:2. The ratio between the present ages of the father and his son is 2:1. What is the ratio of the ages of Father & son 10 years hence?
1. 2:1 2. 19:12 3. 12:7 4. 21:11
9. The sum of the ages of a mother and her daughter is 50 years. Also, 5 years ago, the mother‟s age was 7 times the age of the daughter. The present ages of the mother and daughter
respectively are ________
1. 35 & 15 yrs 2. 38 & 12 yrs 3. 40 & 10 yrs 4. 42 & 8 yrs
10. A man is 4 times as old as his son. Four years hence the sum of their ages will be 43 years. The present age of son is _________
1. 5 yrs 2. 7 yrs 3. 8 yrs 4. 10 yrs
11. Kalyani got married 6 years ago. Today her age is 1 4
1 times her age at the time of marriage.
Her son‟s age is 10
1 times her age. Her son‟s age is _________
1. 2 yrs 2. 3 yrs 3. 4 yrs 4. 5 yrs
12. The difference between the ages of two persons is 10 years, 15 years ago, the elder one was twice as old as the younger one. The present age of the elder son is ________
1. 25 yrs 2. 35 yrs 3. 45 yrs 4. 55 yrs
13. The ratio between the ages of A and B at present is 2:3. Five years hence the ratio of their ages will be 3:4. What is the present age of A?
1. 10 yrs 2. 15 yrs 3. 25 yrs 4. None
14. Mahesh is as much younger to Anil as he is older to Prashant. If the sum of the ages of Anil and Prashant is 48 years, what is the age of Mahesh?
1. 20 yrs 2. 24 yrs 3. 30 yrs 4. None
15. Five years ago, Vinay‟s age was one third of the age of Vikas and now Vinay‟s age is 17 years.
What is the present age of Vikas?
1. 5 yrs 2. 36 yrs 3. 41 yrs 4. 51 yrs
16. The age of Arivind‟s father is 4 times his age. If 5 years ago, father‟s age was 7 times of the age of his son at that time. What is Arivind‟s father‟s present age?
1. 35 yrs 2. 40 yrs 3. 45 yrs 4. 55 yrs
17. 10 years ago, Anitha mother was 4 times older than her daughter, after 10 years, the mother will be twice of the daughter. The present age of Anitha is ________
1. 5 yrs 2. 20 yrs 3. 45 yrs 4. 30 yrs
18. A is twice as old as B. 12 years ago, A was five times old as B. Find the present age of A?
1. 16 yrs 2. 32 yrs 3. 24 yrs 4. 28 yrs
19. The age of the father 8 years ago was 5 times the age of his son. At present the father‟s age is 3 times that of his son. Find the age of father?
1. 48 yrs 2. 36 yrs 3. 46 yrs 4. 58 yrs
20. At present the age of the father is five times that of the age of his son. Three years hence, the father‟s age would be four times that of his son. Find the present ages of the father and the son?
1. 8: 32 2. 45: 9 3. 12;57 4. None
21. The age of Mrs. Anjali is 5 times the age of his son. After 12 years the age of Mrs. Anjali will be only twice the age of his son. Find the present age of Mrs. Anjalis‟s son?
1. 4 yrs 2. 16 yrs 3. 12 yrs 4. 18 yrs
22. 9 years ago Vimal was 5 times the age of Sudarshan. If the present age of Vimal is twice the age of Sudarshan, what will be the total of their present ages?
1. 66 yrs 2. 54 yrs 3. 36 yrs 4. 46 yrs
23. At present the age of the father is 6 times the age of his son, 4 years hence the fathers‟ age would be 5 times that of his son. What is the sum of the present ages of father and his son?
1. 116 yrs 2. 112 yrs 3. 114 yrs 4. 111 yrs
24. At present the age of the father is 7 times the age of the son, 4 years hence the fathers‟ age would be 4 times that of his son. What is the sum of the present ages of father and his son?
1. 21 yrs 2. 24 yrs 3. 28 yrs 4. 32 yrs
25. At present the age of the father is 7 times the age of his son, 6 years hence the fathers‟ age would be 5 times that of his son. What is the sum of the present ages of father and his son?
1. 80 yrs 2. 64 yrs 3. 96 yrs 4. None of these
26. The sum of ages of A and B is 60 years. After 10 years A will be thrice as old as B. Find the difference of their present ages?
1. 30 yrs 2. 40 yrs 3. 10 yrs 4. 50 yrs
27. The sum of the ages of the father and his son is 41 years. After 17 years the father‟s age will be twice the age of his son. Then the respective ages of the father and son are ______ and ____
years.
1. 32, 9 2. 34, 7 3. 33, 8 4. 31, 10
28. The sum of the ages of a son and father is 56 years. After four years, the age of the father will be three times that of the son. Their ages respectively are _____________
1. 12 & 44 yrs 2. 16 & 48 yrs 3. 16 & 42 yrs 4. 18 & 36 yrs
29. The present ages of the father and son are in the ratio 6:1. After 5 years, the ratio will be 13:3.
Find the present age of the son?
1. 24 yrs 2. 28 yrs 3. 32 yrs 4. None
30. The ratio of the present ages of P and Q is 8:5. After 6 years their ages are in the ratio of 3:2.
Find the ratio of the sum and difference of the present ages of P and Q.
1. 13:3 2. 39:19 3. 13:2 4. 13:5
31. 8 years ago, the ratio of the ages of Nagendra and Sunil was 3:2. If the ratio of their present ages is 7:5 respectively, what is the sum of their present ages?
1. 96 yrs 2. 86 yrs 3. 76 yrs 4. 66 yrs
32. The ratio of the ages of A and B at present is 4:2. 10 years earlier, the ratio was 3:2, then find the present ages of A and B.
1. 40 & 30 yrs 2. 48 & 36 yrs 3. 64 & 48 yrs 4. 20 & 15 yrs
33. The ages of Kanchan is thrice the age of the Chandan. After 12 years the age of Kanchan will become twice the age of Chandan. Then the sum of their present ages is ____ years.
1. 42 yrs 2. 48 yrs 3. 46 yrs 4. 50 yrs
34. The age of Jayshree is thrice the age of her younger sister. The product of their ages is 300 years. Then the Jayshree‟s present age is ___________ years.
1. 30 2. 20 3. 10 4. 40
35. At the time of the marriage, a man was 6 years elder than to his wife. 12 years after their marriage, his age is 6/5 times the age of his wife. What was the wife‟s age at the time of marriage?
1. 18 years 2. 24 years 3. 30 years 4. 36 years
36. The difference of present ages of A and B is 12 years. 6 years back their ages were in the ratio 3:2, how old is B?
1. 32 years 2. 35 years 3. 30 years 4. 45 years
37. Siddhika‟s age is 1th
6 of her father‟s age. Siddhika‟s father‟s age will be twice of Kamal‟s age after 10 years. If Kamal‟s 8th birthday was celebrated two years before, then what is Siddhika‟s present age?
1. 10 years 2. 15 years 3. 5 years 4. 3 years
38. 3 years ago, the father‟s age was twice the ages of his 4 daughters. In 3 years time, the father‟s age will be equal to sum of ages of the daughters. Find the present age of father.
1. 45 years 2. 36 years 3. 24 years 4. 39 years
39. Ten years before, one is seven years more than the “half the age” of other. Now the bride‟s age is 30 years. And also one is nineteenths the age of other. What is groom‟s present age.
1. 35 2. 27 3. 40 4. 58
40. When I add 4 times my age 4 years from now to 5 times my age 5 years from now, I get 10 times my current age. How old will I be 3 years from now?
1. 52 2. 40 3. 44 4. None
1) 2 11) 2 21) 1 31) 1
2) 4 12) 2 22) 3 32) 1
3) 2 13) 1 23) 2 33) 2
4) 4 14) 2 24) 4 34) 1
5) 2 15) 3 25) 3 35) 1
6) 4 16) 2 26) 2 36) 3
7) 3 17) 2 27) 3 37) 3
8) 2 18) 2 28) 1 38) 4
9) 3 19) 1 29) 4 39) 2
10) 2 20) 2 30) 1 40) 3