Problems on Ages Questions - 1

Difference between the ages of Sunil and Anil is 4 years and the product of their ages is 672. Find age of Anil, if Anil is younger than Sunil ?
  • 28
  • 32
  • 24
  • 23
  • 31
Explanation   

Let Sunil’s age be x; Anil’s age be y. then,

x - y = 4, xy = 672.

(x + y)2 = (x – y)2 + 4xy.

(x + y)2 = 42 + 4 x 672 => 16 + 2688.

(x + y)2 = 2704 = x + y = 52.

x
+
y
=
52
x
-
y
 
=
4
2x
 
=
56

2x = 56; x = $\displaystyle \frac{56}{2} = 28.$

x = 28 => Sunil age = 28, Anil age = 52 – 28 = 24.

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Age of Kala ranges between 80 and 90, each of her sons have as many sons as they have brothers, their combined number gives age of Kala. What is the age of Kala ?
  • 81
  • 84
  • 90
  • 86
  • 89
Explanation   

Let number of sons be x, then grandsons = x (x – 1).

Age of Kala = x + x2 – x = between 80 and 90 or x2 = between 80 and 90.

The perfect square that lies between 80 and 90 is 81, then age of Kala must be 81.

Note: in such type of questions the age lies between the given ranges of age.

Ex: if range is 60 and 70 the age must be 64 years. which is a perfect square between 60 and 70.

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Meena’s age is thrice that of Sudha’s present age. If age of Sudha is 6 year old, then age of Meena after five years will be ?
  • 22
  • 18
  • 19
  • 21
  • 23
Explanation   

Sucha’s age 6 years, then Meena’s age = 6 x 3 = 18.

After 5 years Meenas age = 18 + 5 = 23 years.

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Jaya’s age is $\displaystyle \frac{3}{4}$th of her husband Amit’s age, but fifteen years ago her age was $\displaystyle \frac{8}{9}$th of Amit’s age. Find Jaya and Amit’s present ages ?
  • 39, 41
  • 39, 42
  • 33, 36
  • 42, 45
  • 45, 48
Explanation   

Let age of Jaya and Amit age 15 years ago be 8x : 9x.

Then present ages = $\displaystyle \frac{8\text{x} \ + 15}{9\text{x} \ + 15} = \frac{3}{4}$ => 32x + 60 = 27x + 45.

5x = 15 => x = 3.

Age of Jaya 15 years ago was 8x = 8 x 3 = 24, Amit = 9x = 9 x 3 = 27.

Present age of Jaya = 24 + 15 = 39; Amit = 27 + 15 = 42.

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If digits of Rita’s age are reversed gets her husband’s age, and difference between the ages is $\displaystyle \frac{1}{11}$th of sum of ages, then age of Rita and her husband respectively is ?
  • 34 and 43
  • 43 and 34
  • 45 and 54
  • 30 and 41
  • 23 and 32
Explanation   

We can find from the options.

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Sum of ages of X and Y is 6 years more than the sum of ages of Y and Z. then Z is how many years younger than X ?
  • 6 years
  • 8 years
  • 4 years
  • 7 years
  • Data inadequate
Explanation   

(X + Y) – (Y + Z) = 6 => X – Z = 6 years.

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Eight years ago average age of son and father was 31 years today, the ratio of their ages is 1 : 2, what is the present age of the father ?
  • 45
  • 54
  • 51
  • 52
  • 53
Explanation   

Sum of ages of son and father 8 years ago = 31 x 2 = 62.

Present sum of ages = (31 + 8) x 2 = 78.

Father = 78 $\displaystyle \times \frac{2}{3}$ = 52.

Son = 78 $\displaystyle \times \frac{1}{3}$ = 26.

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Average age of 18 students is 18, if 12 new students joined the average increases by 0.8 years, find average age of the new students ?
  • 22
  • 18.8
  • 19.6
  • 21
  • 20
Explanation   

Sum of ages = 18 x 18 = 324.

New average = 18.8 years.

Sum of ages including 12 new students = (18 + 12) x 18.8 = 564.

Sum of ages of 12 new students = 564 – 324 = 240.

Average age = $\displaystyle \frac{240}{12}$ = 20 years.

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My brother is one year younger to me, if my brother age is added to my age digits of my age get reversed, and then my age is ?
  • 28
  • 36
  • 37
  • 29
  • 33
Explanation   

From the options we can find, with the help of trial and error method.

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If one year ago the digits of my age are reversed, I get my sons present age. I am thrice as old as my son, what was my son’s age one year ago ?
  • 13
  • 14
  • 16
  • 15
  • 17
Explanation   

From the options we can find, with the help of trial and error method.

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