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Question

A and B are friends and A is older than B by 2 years. A's father D is twice as old as A and B is twice as old as his sister C. The ages of D and C differ by 40 years. Find the ages of A and B.

A
A= 18 years and B= 24 years
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B
A= 42 years and B= 24 years
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C
A= 56 years and B= 24 years
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D
A= 26 years and B= 24 years
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Solution

The correct option is C A= 26 years and B= 24 years
Let age of A=x years
and age of B=y years
Since their age differ by 2 years
xy=2 (i)
Now.
A's father D is twice as old as A
Age of D=2x years and
B is twice as old as his C
Age of C=12ageofB
=12yyears
Again,
Age of D and C differ by 40 years.
=>2xy2=40
=>4xy=80 (ii)
From equation (i) and (ii) we get,
xy=2 (i)
4xy=80 (ii)
- + -
3x=78
=>x=783
=>x=26 years
Putting the value of x in equation (i) we get,
xy=2
=>26y=2
=>y=26+2
=>y=24
Age of A is 26 years and Age of B is 24

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