arithmetic problems on ages questions and answers - skillgun
Raghava's age after 15 years will be four times of that age which was 15 years back. Find his present age.
Solution: Assume Raghava's age be x years, his age 15 years back = x - 15, and age after 15 years = x + 15.
Then according to the problem age after 15 years = a(age 15 years back) i.e.,(x + 15) = 4(x - 15) or x + 15 = 4x -60 or 3x = 75.
.'. x = 25 years.
The ages of two persons differ by 12 years. If 4 years ago, the elder one be 3 times as old as the younger one, find their present ages in years.
Solution: Let the age of the younger person be x years. Then, age of the elder person = (x + 12) years.
.'. 3(x - 4) = (x + 12 - 4) => 2x = 20 => x = 10.
hence the present ages are 10 years and 22 years.
The present age of a mother is 2 years more than three times the age of her son. Three years hence, mother's age will be 8 years more than twice the age of the son. Find the present age of the mother.
Solution: Let the son's present age be x years. Then, mother's present age = (3x + 2) years.
.'. (3x + 2 + 3) = (2(x + 3) + 8)
3x+5=2x+14 => x =9.
hence, mother's present age=3x+2 = 3*9+2 = 29 years.
One year ago, the ratio of Vikram's and Pramod's age was 6 : 7 respectively. Four years hence, this ratio would becomes 7 :8. How old is Pramod ?
Solution: let Vikram's and Pramod's ages one year ago be 6x and 7x respectively. Then, Vikram's age 4 years hence = (6x+1)+4=(6x+5) years.
Pramod's age 4 years hence =(7x+1)+4=(7x+5) years.
------- = ---- <==> 8(6x+5)=7(7x+5) <==> x = 5.
Hence, Pramod's present age=(7x+1) = 36 years.
Kiran is younger than Varun by 6 years. If their ages are in the respective ratio of 3 : 4, How old is Kiran?
Solution: Let Varun's age be x years. Then, Kiran's age=x-6 years.
.'. (X-6)/x = 3/4
Hence, Kiran's age= 24-6 = 18 years.
The ratio between the present ages of A and B is 3 : 4. If B is 6 years old than A, what will be the ratio of the ages OS A and B after 3 years?
Solution: Let A's age and B's age be 3x years and 4x years respectively. Then, 4x-3x=6 <==> x = 6.
.'. Required ratio = (3x+3) : (4x+3) = 21 : 27 = 7 : 9.
The ratio between the present ages of X and Y is 2 : 3. After 4 years, X's age will be 20 years. What is the age of Y at present?
Let the present ages of X and Y be 2x and 3x respectively.
Then, 2x+4 = 20
=> x = 16/2 = 8
.'. Y's present age = 3x = 3*8 = 24 years.
Present ages of Pratyush and Prakash are in the ratio 5 : 4 respectively. Three years hence, the ratio of their ages will become 11 : 9 respectively. What is Prakash's present age in years?
Solution: Let the present ages of Pratyush and Prakash be 5x and 4x years respectively. Then,
------- = ---- <==> x= 6.
.'. Prakash's present age 4x = 4*6 = 24 years.
The ratio of the ages of Kishore and ram 6 years ago was 6 : 5. four years hence, the ratio of their ages will be 11 : 10. what is ram's age at present?
Solution: Let the ages of Kishore and ram 6 years ago be 6x and 5x respectively.
Then, (6x+6)+4 11
------------ = ---- => x= 2.
.'. Ram's present age = (5x+6) =1 6 years.
The ratio of the two boys ages is 5 : 6. the product of their ages is 1470. The ratio of their ages after 7 years will be :
Solution: Let the present ages of the two boys be 5x and 6x years respectively. Then, 5x*6x=1470. <==> 30x^2 = 1470 <==> x^2 = 49 => x = 7.
.'. Required ratio =(5x+7) : (6x+7) = 42 : 49 = 6 : 7.
The ratio between the present ages of A and B is 3 : 5 respectively. The ratio between A's age 2 years ago and B's age 8 years hence is 1 : 2. What is the ratio between A's age 2 years hence and B's age 8 years age?
Solution: Let the present ages of A and B be 3x and 5x years respectively.
Then, 3x-2 1
------- = ----
Required ratio = (3x+2) : (5x -8) = 19 : 26
X is three years younger than Y who is twice as old as Z. if the total of the ages of X, Y and Z be 22, then how old is Y?
Solution: Let Z's age be x. then, Y's age=2x years. And X's age=(2x-3).
.'. (2x-3)+2x+x=22. ,==> x = 5.
Hence, Y's age= 2*5=10 years.
A women is 21 years older than her son. In two years, her age will be twice the age of her son. The present age of the son is:
Solution: Assume the son's present age be x years. Then, women's present age=x+21 years.
.'. (x+21)+2=2(x+2) ==> x =19.
Thirteen years ago, a father was three times as old as his son. Now the father is only twice as old as his son. Then the sum of the present ages of the son and the father is :
Solution: Let the present ages of the father and son be 2x and x respectively. Then, (2x-13) = 3(x-13) <==> x= 26.
.'. Required sum = 2x+x = 3x = 3*26 = 78 years.
A daughter's present age is two-fifth of the age of her mother. After 8 years, she will be one-half of the age of her mother. How old is the mother at present?
Solution: Assume the mother's present age be x years. Then, the daughter's present age =(2x/5) years.
.'. (2x/5 + 8) = 1/2(x+8) <=> x=40. Hence, mother's present age is 40 years.
Manju's grandfather was 8 times older to her 16 years ago. He would be 3 times of her age 8 years from now. Eight years ago, what was the ratio of Manju's age to that of her grandfather ?
Solution: 16 years ago, let Manju's age=x years and grandpa = 8x years.
After 8 years from now, Manju=x+16+8 years and grandpa=8x+16+8 years.
.'. 8x+24=3(x+24) => 5x=48.
8 years ago, Manju x+8 48/5 + 8 88 11
---------- = ------ = -------------- = ------ = ---- .
grandpa 8x+8 8*48/5 + 8 424 53
The total age of P and Q is 17 years more than the total age of Q and R. R is how many years younger than P?
R is elder than P
Solution: (P + Q) - (Q + R) = 17 => P - R = 17.
Hence, R is 17 years younger than P.
Manoj got married 8 years ago. His present age is six-fifth times his age at the time of his marriage. Manoj's sister was 10 years younger to him at the time of his marriage. The age of Manoj's sister is:
Solution: Let Manoj's present age be x years. Then, his age at the time of marriage = (x-8) years.
.'. x = 6(x-8)/5 => 5x = 6x -48 <==> x =48.
Manoj's sister present age = (30+8) years = 38 years.
Mother is aged three times more than her son Suraj. After 3 years, she would be two and a half times of suraj's age. After further 5 years, how many times would she be of Suraj's age?
Solution: let Suraj's present age be x years. Then, mother's present age = (x+3x) years = 4x years.
.'. (4x+3) = 5(x+3)/2 <=> 8x+6=5x+15 <=> x = 3.
Hence required ratio = (4x+8)/(x+8) = 20/11.
A man was asked to state his age in years. His reply was, " Take my age five years hence, multiply it by 4 and and then subtract four times my age three years ago and you will know how old I am." what was the age of the person?
Solution: Let the present age of the man be x years.
Then, 4(x+5)-4(x-3) = x
=> x = 32.
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