A and B are the freinds and their ages differ by 2 years. A is father D is twice as old as A and B is as old as his sister C. The age of D and C differ by 40 years. Find the ages of A and B
Answers
Answer:
Let the age of A,B,C and D are p,q,r, and s respectively.
Given:-
∣p−q∣=2
t=2p ⇒p=
2
t
q=2s
∣t−s∣=40⟶eq
n
(i)
According to the question
D is father of A
C is sister of B
⇒ D is elder than C
∴eq
n
(i) can be written as-
t−s=40 ⟶eq
n
(ii)
Case I:-
A is elder than B
∴ p−q=2 [Given]
As th value of p and q is given in terms of s and t,
2
t
−2s=2
Multiplying both sides by 2 in above equation, we get
t−4s=4⟶eq
n
(iii)
On subtracting eq
n
(iii) from (ii), we get
⇒t−st+4s=40−4
⇒ s=12
On substituting the value of s in eq
n
(ii), we get
⇒t−12=40
⇒ t=52
As given,
p=
2
t
⇒p=26
q=2s⇒q=24
Therefore, Ages of A and B are 26 and 24 respectively.
Case II:-
B is elder than A
∴ q−p=2 [Given]
As th value of p and q is given in terms of s and t,
2s−
2
t
=2
Multiplying both sides by 2 in above equation, we get
4s−t=4⟶eq
n
(iv)
On adding eq
n
(ii)&(iv), we get
⇒t−s+4s−t=40+4
⇒ 3s = 44
⇒s=
3
44
On substituting the value of s in eq
n
(ii), we get
⇒t−
3
44
=40
⇒t=
3
164
As given,
p=
2
t
⇒p=
6
164
=27
3
1
q=2s⇒q=
3
88
=29
3
1
Therefore, Ages of A and B are 27
3
1
and 29
3
1
Hence, (A) is correct answer.respectively