Practice Exercise 1:

A, B, C, D, E, F and G are brothers.

Two brothers had an argument and A said to B, “You are as old as C was when I was as old as D and will be as old as E was when he was as old as C is now.”

B said to A, “You may be older than E but G is as old as I was when you were as old as G is and D will be as old as F was when F will be as old as G is.”

1. Who is the eldest brother?

A. A

B. E

C. C

D. Cannot be determined

2. Who is the youngest brother?

A. B

B. D

C. F

D. Cannot be determined

3. Who two are probably twins?

A. D and G

B. E and C

C. A and B

D. Cannot be determined

4. Which of the following is false?

A. G has four elder brothers

B. A is older than G but younger than E

C. B has three elder brothers

D. There is a pair of twins among the brothers

Let’s analyze the statements of both the brothers.

> A to B:

You are as old as C was when I was as old as D”

B’s present age equals to C’s past age when A was of D’s present age. This means C is elder than B and A is elder than D.

C > B and A > D

“You will be as old as E was when he was as old as C is now.”

B’s age will be equal to E’s past age when E’s age equaled C’s present age. This means E is elder than both B and C.

E > C > B

> B to C:

“You may be older than E but G is as old as I was when you were as old as G is”

This implies A may or may not be elder than E.

G’s present age equals B’s past age when A’s past age was of G’s present age. Suppose the current age of G is 10 years. Therefore, G’s present age equals B’s past age when A was 10 years old. This means B’s past age was also 10 years old and A and B are twins.

E > C > B = A > G

“D will be as old as F was when F will be as old as G is”

This implies G is elder than F and F is elder than D.

E > C > B = A > G > F > D

1. E is the eldest brother. So, B is the correct option.

2. D is the youngest brother. So, B is the correct option.

3. A and B are twins. So, C is the correct option.

4. B has only two elder brothers. So, C is the correct option.

Practice Exercise 2: A joint family consists of seven members A, B, C, D, E, F and G with three females. G is a widow and sister-in-law of D’s father F. B and D are siblings and A is daughter of B. C is cousin of B. Who is E?

1. Wife of F

2. Grandmother of A

3. Aunt of C

Select the answer using the code given below:

A. 1 and 2 only

B. 2 and 3 only

C. 1 and 3 only

D. 1, 2 and 3

Blood Relation Tree:

> B and D are siblings. F is D’s father and A is B’s daughter. G is the sister-in-law of F and is a widow. This means that G is a female. > Since C is B’s cousin, C must be the child of G. E must be F’s wife. Since are three females in the family, B, D and C are males. Clearly, E is F’s wife, A’s grandmother and Aunt of C. Therefore, D is the correct option.

Practice Exercise 3: Amit, Bharat, Chandan, Dinesh, Eeshwar and Ferguson are cousins. None of them are of the same age, but all of them have birthdays on the same date. The youngest of them is 17 years old and Eeshwar who is eldest, is 22 years old. Ferguson is somewhere between Bharat and Dinesh in age. Amit is elder to Bharat and Chandan is older than Dinesh.

1. Which of the following is not possible?

A. Dinesh is 20 years old

B. Ferguson is 18 years old

C. Ferguson is 19 years old

D. Ferguson is 20 years old

2. If Bharat is 17 years old, then which of the following could be the ages of Dinesh and Chandan, respectively?

A. 18 and 19

B. 19 and 21

C. 18 and 20

D. 18 and 21

3. If two of the cousins are between Chandan and Ferguson in age, then which of the following must be true?

A. Amit is between Ferguson and Dinesh in age

B. Bharat is 17 years old

C. Bharat is younger than Dinesh

D. Ferguson is 18 years old

4. If Amit is one year elder to Chandan, then the number of logically possible orders of all six cousins by increasing age is

A. 2

B. 3

C. 4

D. 5

There are 6 cousins. The eldest is 22 years old and the youngest is 17 years old. None of them have the same age, but all of them have birthdays on the same date. This implies that the ages of remaining cousins are 18 years, 19 years, 20 years, 21 years and 22 years.

Suppose that Bharat is elder to Dinesh.

> Then Ferguson, Amit and Chandan are also older than Dinesh. This implies that Dinesh is 17 years old.

> Since Amit is elder to Bharat and Ferguson is somewhere between Bharat and Dinesh in age, Bharat’s age can be either 19 years or 20 years. Suppose that Dinesh is elder to Bharat

> This would mean that Bharat is 17 years old.

> Since Chandan is elder to Dinesh and Ferguson is somewhere between Bharat and Dinesh in age, Dinesh’s age can be either 19 years or 20 years.  