Question 1 :
Now Sharma's age is quarter as old as his father. Six years ago, the father's age was seven times as old as Sharma. Find their present ages
(A) 8, 32 (B) 10, 40 (C) 12, 48 (D) 14, 56
Answer :
Let f and s be the present ages of father and Sharma.
Given : Now Sharma's age is quarter as old as his father.
f = 4s ----(1)
Given : Six years ago, the father's age was seven times as old as Sharma.
f - 6 = 7(s - 6)
f - 6 = 7s - 42
f = 7s - 36
Substitute f = 4s.
4s = 7s - 36
-3s = -36
s = 12
Substitute s = 12 into (1).
f = 4(12) = 48
The present ages of Sharma and his father are 12 and 48 respectively.
The correct answer choice is option (C).
Question 2 :
The ratio of the present ages of Muthu and Karthick is 5 : 3. Six years ago, their ages were in the ratio 3 : 1. What will the ratio of their ages be, after 6 years?
(A) 5 : 4 (B) 10 : 7 (C) 10 : 8 (D) 4 : 3
Answer :
Given : The ratio of the present ages of Muthu and Karthick is 5 : 3.
From the above ratio,
present age of Muthu = 5x
present age of Karthick = 3x
Six years ago,
age of Muthu = 5x - 6
age of Karthick = 3x - 6
Six years ago, the ratio between their ages was
= (5x - 6) = (3x - 6) ----(2)
Given : Six years ago, the ratio between their ages was
= 3 : 1 ----(2)
From (1) and (2),
(5x - 6) = (3x - 6) = 3 : 1
5x - 6 = 3(3x - 6)
5x - 6 = 9x - 18
-4x = -12
x = 3
present age of Muthu = 5(3) = 15
present age of Karthick = 3x = 3(3) = 9
After 5 years,
age of Muthu = 15 + 5 = 20
age of Karthick = 9 + 5 = 14
After 6 years, the ratio of their ages will be
= 20 : 14
= 10 : 7
The correct answer choice is option (B).
Question 3 :
A father is now twice as old as his son. Twenty years ago, he was six times as old as his son. What are their ages now?
(A) 60, 30 (B) 40, 20 (C) 58, 29 (D) 50, 25
Answer :
Let f and s be the rpesent ages of father and son respectively.
Given: A father is now twice as old as his son.
f = 2s ----(1)
Given : Twenty years ago, he was six times as old as his son.
f - 20 = 6(s - 20)
f - 20 = 6s - 120
f = 6s - 100
Substitute f = 6s - 100 into (1).
2s = 6s - 100
-4s = -100
s = 25
Substitute s = 25 into (1).
f = 2(25) = 50
The present ages of father and son are 50 years and 25 years respectively.
The correct answer choice is option (D).
Question 4 :
At present, Abi is twice as old as Reeta. After seven years, if their age difference be 5 years. then the present age of Reeta is
(A) 5 (B) 7 (C) 9 (D) 10
Answer :
Let a and r be the rpesent ages of Abi and Reeta respectively.
a = 2r
Given : After seven years, if their age difference be 5 years.
(a + 7) - (r + 7) = 5
a + 7 - r - 7 = 5
a - r = 5
Substitute a = 2r.
2r - r = 5
r = 5
The present age of Reeta ias 5 years.
The correct answer choice is option (A).
Question 5 :
A boy is now twice as old his sister, four years ago, he was thrice as old as her. What are their ages now?
(A) 18, 9 (B) 14, 7 (C) 16, 8 (D) 12, 6
Answer :
Let b and s be the rpesent ages of the boy and his sister.
Given : The boy is now twice as old his sister.
b = 2s ----(1)
Given : Four years ago, the boy was thrice as old as his sister.
b - 4 = 3(s - 4)
b - 4 = 3s - 12
b = 3s - 8
Substitute b = 2s.
2s = 3s - 8
-s = -8
s = 8
Substitute s = 8 into (1).
b = 2(8) = 16
The present ages of the boy and his sister are 16 and 8 respectively.
The correct answer choice is option (C).
Question 6 :
Three years ago, the average age of a family of 5 members was 17 years. A baby having been born and the average age of the family is the same today. The present age of the baby is
(A) 1 year (B) 1½ years (C) 2 years (D) 3 years
Answer :
Given : Three years ago, the average age of a family of 5 members was 17 years.
That is,
sum of the ages of 5 members (3 years ago) = 17 ⋅ 5
sum of the ages of 5 members (3 years ago) = 85
At present, each member's age is increased by 5 years.
Sum of the present ages of 5 members :
= 85 + 5 ⋅ 3
= 85 + 15
= 100
Let x be the present age of the baby.
Sum of the present ages of 5 members and 1 baby :
= 100 + x
Given : The average age of the family is the same today as three years ago.
That is,
100 + x = 17 ⋅ 6
100 + x = 102
x = 2
The present age of the baby is 2 years.
The correct answer choice is option (C).
Question 7 :
The sum of the ages of a son and father is 72 years. After 12 years, the age of the father will be three times that of the son. What is the age of the son now?
(A) 12 (B) 22 (C) 14 (D) 16
Answer :
Let s and f be the present ages of father and son.
Given : The sum of the ages of the san and father is 72 years.
s + f = 72
f = 72 - s
Given : After 12 years, the age of the father will be three times that of the son.
f + 12 = 3(s + 12)
Substitute f = 72 - s.
72 - s + 12 = 3(s + 12)
72 - s + 12 = 3s + 36
-s + 84 = 3s + 36
-4s = -48
s = 12
The age of the son is 12.
The correct answer choice is option (A).
Question 8 :
B is twice as old as A, but twice as young as F. C is half the age of A, but twice the age of D. Which two persons form the pair of the oldest and youngest?
(A) F and A
(B) D and F
(C) B and F
(D) F and C
Answer :
Let x be the age of A.
Given : B is twice as old A.
Age of B = 2x
Given : B is twice as young as F.
That is, F is twice as old as B.
Age of F = 2(2x) = 4x
Given : C is half the age of A.
Age of C = ˣ⁄₂
Given : C is twice the age of D.
That is, D is half the age of C.
Age of D = ½(ˣ⁄₂)
Age of D = ˣ⁄₄
List of the ages of all the five people.
Age of A = x
Age of B = 2x
Age of C = ˣ⁄₂
Age of D = ˣ⁄₄
Age of F = 4x
Clearly D is the youngest and F is the oldest.
The correct answer choice is option (B).
Question 9 :
Latha is a year older than Sunitha. Sunitha is two years older than Bindu. Rajan is a year older than Bindu. Who is the youngest of all?
(A) Sunitha
(B) Latha
(C) Bindu
(D) Rajan
Answer :
Since the ages of two people Sunitha and Bindu are linked to the age of Bindu, we can assign a variable for Bindu's age.
Let x be the ange of Bindu.
Given : Sunitha is two years older than Bindu. Rajan is a year older than Bindu.
Age of Sunitha = x + 2
Age of Rajan = x + 1
Given : Latha is a year older than Sunitha.
Age of Latha = (x + 2) + 1 = x + 3
List of the ages of all the four people.
Age of Bindu = x
Age of Rajan = x + 1
Age of Sunitha = x + 2
Age of Rajan = x + 3
Clearly Bindu is the youngest of all.
The correct answer choice is option (C).
Question 10 :
I. Tanya is older than Eric.
II. Cliff is older than Tanya
III. Eric is older than Cliff.
If the first two statements are true, the third statement is
(A) True
(B) False
(C) Uncertain
(D) Certain
Answer :
Let t, e and c be the ages of Tanya, Eric and Cliff.
I. Tanya is older than Eric.
t > e ----(1)
II. Cliff is older than Tanya
c > t ----(2)
From(1) and (2), we have
c > t > e
According to the question, c > t > e is true.
That is, Cliff is older than both Tanya and Eric.
III. Eric is older than Cliff.
e > c
The third statement says that Eric is older than Cliff.
Clearly, the third statement is false.
The correct answer choice is option (B).
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