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# Arithmetic Aptitude :: Problems on Ages

Home > Arithmetic Aptitude > Problems on Ages > General Questions

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11. Ram is 42 years old and Rajesh is 58 years old.How many years ago was the ratio of their ages 4:6

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Explanation:

Lets assume x years ago their ratio is 4:6

so (42-x)/(58-x) = 4:6
=> 6*(42-x) = 4*(58-x)
=> (252 - 6x) = (232 - 4x)
=> 2x = 20 => x =10

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12. The ratio between the P and Q age is 7: 9. If the difference between the present ages of Q and P's age after 4 years is 2 then what is the total of the present ages of P and Q?

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Explanation:

As per Formula:
(If the given ages in a ratio a : b then age will be ax and bx)

So age of P will be 7x and Q will be 9x
As per the question:
(9x - 7x) +4 = 2,
=> x = 3
=> P present age will be = 21, Q age will be = 23
So Total of their Present age = 27 + 21 = 48

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13. The ratio of the ages of priya and riya is 2:5. After 8 years, their ages will be in the ratio of 2:3. Then the sum of their present ages

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Explanation:

As per Formula:
(If the given ages in a ratio a : b then age will be ax and bx)

so priya age = 2x and riya age = 5x.
So After 8 years their age ratio
(2x + 8)/(5x + 8) = 2/3
=> 6x + 24 = 10x + 16
=> 4x = 8
=> x = 2
so priya age will be 4 years and riya age will be 10 years

So their sum of age (priya and riya) = 14

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14. The ratio of the ages of two persons are in the ratio of 5:7 and the difference between their ages is 18 years. Find the sum of the ages of the persons after 5 years,

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Explanation:

As per Formula:
(If the given ages in a ratio a : b then age will be ax and bx)

=> 7x - 5x = 18
=> 2x = 18 => x = 9

so Their age is 45 and 63 after 5 year their age will be 50 and 68
sum of age = 50 + 68 = 118 years.

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15. If P age is twice the average age of P, Q and R ages. Q's age is one half the average of P, Q and R's age. If the age of R is 5 years, then find the sum of ages of P, Q and R.

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Explanation:

P = 2*(P + Q+ R)/3 --------(1)
Q = (1/2)*(P + Q+ R)/3 ------- (2)
and R = 5 -----------(3)
By solve the above equations,
=> P = 20, Q = 5 and R = 5
Sum of their ages = P+Q+R = 20 + 5 + 5 = 30 years.

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16. The sum of the age of mother and daughter is 100 years. 5 years ago their age were in the ratio of 2:1. The ratio of the age of daughter and mother after 10 years

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Explanation:

As per Formula:
(If the given ages in a ratio a : b then age will be ax and bx)

Five year ago mother age = 2x years and daughter age = x years
Sum of their present ages = (2x+5) + (x+5) = 100
=> 3x + 10 = 100
=> x = 90/3 => x = 30
Present age of mother and daughter is 65 and 35 years respectively.

After 10 years ratio of daughter and mother ages = (35+10)/(65+10)
= 45/75 = 3/5

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17. If 6 is subtracted from the present age of Ritu and the remainder is divided by 6, then the present age of Sheema is obtained. If Sheema is 4 years younger to raju whose age is 12 years, then find the age of Ritu

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Explanation:

Lets assume Ritu present age = x years
so sheema age = (x-6)/6 years

As per question:
sheema age [(x-6)/6 + 4] = 12
(x-6)/6 = 12 - 4
=> (x-6)/6 = 8
=> x - 6 = 48 => x = 54

So Ritu age = 54 years.

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18. The difference between the age of the two persons is 6 years.Twelve years ago, the elder was thrice as old as the younger one.The present age of the elder

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Explanation:

Lets assume elder present age is x years and younger age is y years.

As per question
x - y = 6 -------------- (1)

twelve years ago
(x-12) = 3 *(y-12)
=> 3y - x = 36-12
=> 3y-x = 24 ------- (2)

By solving the eq (1) and (2)

2y = 30 => y = 15 and x = 21

so elder age is 21 years.

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19. In 8 years ago P will be twice as old as Q.If P is now 6 years older than Q,then the present age of Q

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Explanation:

Lets P preset age is x year and Q present age is y years.

so 8 Year ago
(x-8) = 2(y-8)
=> 2y - x = 8 ------------------ (1)

6 years older
x = y+6
=> x - y = 6 ------------- (2)
By solving the eq (1) and (2)
y = 14 and x = 20

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20. The age of Vivek is 54yrs, If shyam's age is 36% more than that of Vivek, What % is Vivek's age less than Shyam ?

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