Below are three problems based on the concept of number of brothers and sisters, you have to find the number of siblings according to given statements.
Question 1 :
If Mr.X, Mr.Y and Mr.Z are three siblings and following three statements are true
1) Mr.X has one older brother and three younger sisters.
2) Mr.Y has two older brothers and two younger sisters
3) Mr.Z has three older brothers and one younger sister.
Then the least possible number of siblings in their family is:
a) 5 b) 6 d) 7 d) 8
Solution :
First, we need to think about X, Y and Z as who is the oldest among the three and who is the youngest among the three.
X has one older brother while Y has two. Therefore, X is older than Y. Similarly Y is older than Z. Therefore, among X,Y and Z
X is the oldest, Y is next and Z is the youngest.
X has an older brother and Z has a younger sister.
Try making a chart laying out all the three conditions given in question, and mark the gender of each known sibling.
Then, it is clear that X is male and Y is female.
``` M M F M F F
1st 2nd 3rd 4th 5th 6th
X Y  Z```
Based on the above chart, there should be at least 6 siblings.
Question 2:
If A, B and C are triblet. A,C are males and B is female,
1) A & C say " We have 2 more brothers than the number of sisters"
2) B says " I have 2 more brothers than twice the sisters "
If the above two statements are true then the number of siblings in their family is:
a) 6 b) 12 c) 8 d) 9
Solution :
Let g be the number of girls in the family.
Let b be the number of boys in the family.
Consider statement 1, A and C would have b-2 brothers (excluding them). This b-2 is equal to two more than the number of sisters they have.
Therefore, b-2 = g+2
Or, b-g = 4 -----(1)
Now, from statement 2, B would have g-1 sisters (excluding herself) and b brothers. She has 2 more brothers than twice the number of sisters.
Therefore, Twice the number of sisters = 2(g-1) which is equal to 2 + number of brothers.
Then we have, 2(g-1) + 2 = b
2g - 2 + 2 = b
b-2g = 0 -------(2)
Solving (1) and (2), we have g = 4 and b = 8.
Hence the number of siblings = 4+8 = 12.
Question 3 :
Aravind and Bavya are friends.
1)Aravind's sister has thrice as many sisters of Bavya as brothers.
2)Aravind has 1 more brother than than that of Bavya
3)Twice Bavya's brother's sisters equals the number of boys in Aravind's family.
If the above all 3 statements are true then the number of brothers what Aravind has more than Bavya is:
a) 1 b) 2 c) 3 d) none of these
Solution :
Let the number of boys in Aravind's family be a
Let the number of girls in Aravind's family be b
Let the number of boys in Bavya's family be c
Let the number of girls in Bavya's family be d.
consider statement 1, "Aravind's sister has thrice as many sisters of Bavya as brothers" :
Number of Bavya's sisters = d-1 (excluding her)
Thrice the Bavya's sisters = 3(d-1)
Aravind's sister has 'a' number of brothers.
Therefore, 3(d-1) = a
d-1 = a/3....(1)
Consider statement2,"Aravind has 1 more brother than that of Bavya" :
Number of Aravind's brothers = a-1
Number of Bavya's brother = c
Since, Aravind has 1 more brother than Bavya then a-1 = c+1
a-c = 2...(2)
Consider statement3,"Twice Bavya's brother's sisters equals the number of boys in Aravind's family"
The number of sisters of Bavya's brother = d
Number of boys in Aravind's family = a
Therefore 2d = a
Or d = a/2
Then, d-1 = a/2 - 1 ...(3)
Now, let us solve equations we obtained in previous steps :
From (1) and (3),
a/3 = a/2 - 1
a = 6
Put a value in (2), we have c = 4
Put a value in (3), we have d = 3
Therefore Aravind has a-1 = 6-1 = 5 brothers
And Bavya has c = 4 brothers.
Hence, Aravind has 1 more brother than Bavya.