Solve 1) A and B are friends and their ages differ by 2 years. A's father D is twice as old as A and B is twice as old as his sister C. The age of D and C differ by 40 years. Find the ages of A and B
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Solve 1) A and B are friends and their ages differ by 2 years. A's father D is twice as old as A and B is twice as old as his sister C. The age of D and C differ by 40 years. Find the ages of A and B
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Answer:
ANSWER
Let the ages of A and B be x and y years respectively. Then,
x−y=±2 [Given]
D's age =2x years and, C's age =
2
y
years.
Clearly, D is older than C
2x−
2
y
=40⇒4x−y=80
Thus, we have the following two systems of linear equations
x−y=2 .(i)
and, 4x−y=80 (ii)
or
x−y=−2 (iii)
and, 4x−y=80 ..(iv)
Substracting equation (i) from equation (ii), we get
3x=78⇒x=26Putting x=26 in equation (i), we get y=24
or
Substracting equation (iv) from equation (iii), we get
−3x=−82⇒x=
3
82
=27
3
1
Putting x=
3
82
in equation (iii), we get
y=
3
82
+2=
3
88
=29
3
1
Hence, A's age =26 years and B's age =24 years
or
A's age =27
3
1
years and B's age =29
3
1
years.
Answer:
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