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21. The ratio of the ages of the father and the son at present is 3:1. Four years earlier, the ratio was 4:1. What is the sum of the present ages of the son and the father?
  A.  50 years
  B.  46 years
  C.  48 years
  D.  38 years
     
   
View Answer

Shortcut:
If the ratio of the ages of X and Y at present is a : b. 't' years earlier, the ratio was c : d, then the sum of the present ages of X and Y is (a + b)
[
t(c − d) / b x c − a x d
]

Here, a = 3, b = 1, t = 4, c = 4, d = 1
Using these values in the shortcut, we get:
Sum of ages = (3 + 1)
[
4(4 − 1) / 1 x 4 − 3 x 1
]

= 4
[
4 x 3 / 4 − 3
]
= 4
[
4 x 3 / 1
]
= 4 x 4 x 3 = 48
Hence, the sum of ages of father and son is 48 years.

22. A man's age is 125% of what it was 10 years ago, but 83
1 / 3
% of what it will be after 10 years. What is his present age?
  A.  52 years
  B.  48 years
  C.  54 years
  D.  50 years
     
   
View Answer

Shortcut:
If a man's age is a% of what it was t1 years ago, but b% of what it will be after t2 years. Then his present age is
at1 + bt2 / a − b
years.
If t1 = t2, then formula will become
[
a + b / a − b
]
t
Here, a = 125, t1 = t2 = 10, b = 83
1 / 3
or
250 / 3

Using these values in the shortcut, we get:
Present age =
[
125 + 250/3 / 125 − 250/3
]
10
=
[
(375 + 250)/3 / (375 − 250)/3
]
10
=
625 / 125
x 10 = 5 x 10 = 50
Hence, his present age is 50 years.

23. The ratio of A's and B's ages is 4 : 5. If the difference between the present age of B and the age of A 5 years hence is 3, then what is the total of present ages of A and B?
  A.  72 years
  B.  70 years
  C.  62 years
  D.  75 years
     
   
View Answer

Shortcut:
The ratio of X and Y ages is a : b. If the difference between the present ages of X and Y 't' years hence is 'z' then (i) the present age of X (younger) =
t + z / b/a − 1
years.
(ii) the present age of B (older) =
(t + z)b/a / b/a − 1
years
(iii) the sum of the present ages of X and Y =
t + z / b/a − 1
[
1 + b/a
]
years. Note: Here X is always younger than Y and a : b is younger : older ratio Hence, b/a = older/younger Here, a = 4, b = 5, t = 5, z = 3
Using these values in the shortcut, we get:
Sum of their ages =
5 + 3 / 5/4 − 1
[
1 + 5/4
]

=
8 / 1/4
[
(4 + 5)/4
]

= 8 x 4 x
9 / 4

= 32 x
9 / 4
= 8 x 9 = 72
Hence, the sum of ages of A and B is 72 years.

24. The difference of present ages of A and B is 12 years. If 6 years back their ages were in the ratio 3 : 2, how old are A and B?
  A.  A's age: 40 years; B's age: 28 years
  B.  A's age: 42 years; B's age: 30 years
  C.  A's age: 44 years; B's age: 32 years
  D.  A's age: 45 years; B's age: 33 years
     
   
View Answer

Shortcut:
The difference of present ages of X and Y is 'z' years. If 't' years back their ages were in the ratio a:b, then (i) the age of X =
[
t +
z / a/b − 1
]
+ z years.
(ii) the age of Y =
[
t +
z / a/b − 1
]
years
(iii) the sum of ages of X and Y =
[
2(t +
z / a/b − 1
+ z
]
years.
Note: Here X > Y, i.e X is older than Y.
Hence a > b
Here, a = 3, b = 2, t = 6, z = 12
Using these values in the shortcut, we get:
Age of A =
[
6 +
12 / 3/2 − 1
]
+ 12
=
[
6 +
12 / (3 − 2)/2
]
+ 12
=
[
6 +
12 / 1/2
]
+ 12
= 6 + 24 + 12 = 42
Hence, the of ages of A is 42 years.
Age of B =
[
6 +
12 / 3/2 − 1
]
years
=
[
6 +
12 / (3 − 2)/2
]
years
=
[
6 +
12 / 1/2
]
years = 6 + 24 = 30
Hence, the age of B is 30 years.

25. If the ages of P and R are added to twice the age of Q, the total becomes 59. If the ages of Q and R are added to thrice the age of P, the total becomes 68. And if the age of P is added to thrice the age of Q and thrice the age of R, the total becomes 108. What is the age of P?
  A.  14 years
  B.  10 years
  C.  13 years
  D.  12 years
     
   
View Answer

P + R + 2Q = 59
Q + R + 3P = 68
or, Q + R = (68 − 3P) ............... eq1
and P + 3(Q + R) = 108 ................. ...eq2
Putting the value of value of (Q+R) in eq2, we get:
P + 3(68 − 3P) = 108
P + 204 − 9P = 108
204 − 8P = 108
204 − 108 = 8P
8P = 96
P = 12
Hence, the age of P = 12 years.

26. Jay is twice as old as Vikas and half as old as Sumit. If the sum of Sumit's and Vikas's ages is 85 years, what is Jay's age in years?
  A.  34 years
  B.  36 years
  C.  32 years
  D.  30 years
     
   
View Answer

Jay : Vikas : Sumit = 2 : 1 : 4
∴ Jayesh's age =
2 / 1 + 4
x 85 = 34 years

27. The ratio of the present ages of a son and his father is 1:5 and that of his mother and fathe is 4:5. After 2 years the ratio of the age of the son to that of his mother becomes 3:10. What is the present age of the father?
  A.  Son's age: 6 years; Father's age:30 years
  B.  Son's age: 8 years; Father's age:40 years
  C.  Son's age: 7 years; Father's age:35 years
  D.  Son's age: 5 years; Father's age:25 years
     
   
View Answer

S / F
=
1 / 5

⇒ F = 5S
M / F
=
4 / 5

⇒ M =
4 / 5
F
S+2 / M+2
=
3 / 10

⇒ 10S + 20 = 3M + 6
= 3 x
4 / 5
x 5S + 6
= 12S + 6
∴ 2S = 14
⇒ S = 7
∴ F = 5S = 5 x 7 = 35 years.

28. 15 years hence, A will be twice as old as B, but five years ago A was 4 times as old as B. Find the difference of their present ages.
  A.  32 years
  B.  30 years
  C.  34 years
  D.  38 years
     
   
View Answer

Let A's age = m
B's age = n
As per the first condition
(m + 15) = 2 (n + 15)
m − 2n = 15 ...........eq1
As per second condition
(m − 5) = 4 (n − 5)
m − 4n = 15 .............. eq2
Solving eq1 & eq2, we get
m = 45
n = 15
Hence, Age of A = 45 years
Age of B = 15 years.

29. Sandy was twice as old as Amit 10 years back. How old is Amit today if Sandy will be 40 years old 10 years hence?
  A.  24 years
  B.  22 years
  C.  18 years
  D.  20 years
     
   
View Answer

Let Amit's age 10 years back be m years
Then, Sandy age 10 years back = 2m years
∴ 2m + 20 = 40
m = 10
Amit's present age = 10 + 10 = 20 years.

30. The sum of the ages of a father and son is 45 years. Five years ago, the product of their ages was four times the father's age at that time. The present age of the father is:
  A.  34 years
  B.  38 years
  C.  36 years
  D.  32 years
     
   
View Answer

Let father's present age = m years
Then, Son's present age = (45 − m) years
(m − 5)(45 − m − 5) = 4(m − 5)
or m2 − 41m + 180 = 0
(m − 36)(m − 5) = 0
∴ m = 36 years

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