5 years ago,A was thrice as old as B and 10 years later A shall be twice as old as B . what is percent age of A 20 aur 50 or 60 or 40
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5 years ago,A was thrice as old as B and 10 years later A shall be twice as old as B . what is percent age of A 20 aur 50 or 60 or 40
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Step-by-step explanation:
Five years ago, A was thrice as old as B
Let present age of A be x years and the present age of B be y years
Five years ago their ages A's age x - 5 and B's age y - 5
(x - 5) = 3 (y - 5)
x - 5 = 3y - 15
x = 3y - 10….. Eq. 1
Ten years later, A shall be twice as old as B, Thus ten years later their ages will be x + 10 and y + 10
(x +10) = 2 (y + 10)
x + 10 = 2y + 20
x - 2y = 20 - 10
x - 2y = 10…. Eq..2
Substituting value of x from Eq..1 to Eq..2
(3y - 10) - 2y = 10
3y - 2y = 10 + 10
y = 20
The age of B is 20 years
Now substituting the value of y in Eq..2 to derive value of x
x - 2y = 10
x - 2 (20) = 10
x - 40 = 10
x = 10 + 40
x = 50
Thus the age of A is 50 years and age of B is 20 years.The sum of their ages
A + B = 50 + 20 = 70 years
Sum of their ages is 70 years
Answer the age of A is 50 years and age of B is 20 years and sum of their ages is 70 years
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Given :-
To find :-
Solution :-
Let the present age of B be x years
and present age of A be y years.
then,
Case I,
[tex]\bf\dag{\underline{Five\:years\:ago}}:-[/tex]
According to the question,
(y - 5) = 3(x - 5)
⤇ y - 5 = 3x - 15
⤇ -5 + 15 = 3x - y
⤇ 10 = 3x - y
⤇ 3x - y = 10 ..................................(i)
Case II,
[tex]\bf\dag{\underline{Ten\:years\:later}}:-[/tex]
According to the question,
(y + 10) = 2(x + 10)
⤇ y + 10 = 2x + 20
⤇ 10 - 20 = 2x - y
⤇ -10 = 2x - y
⤇ 2x - y = -10 .....................................(ii)
Subtracting eq (ii) from eq (i),
(3x - y) - (2x - y) = 10 - (-10)
⤇ 3x - 2x - y - (-y) = 10 + 10
⤇ x - y + y = 20
⤇ x = 20
putting the value of x in equation (i),
3x - y = 10
⤇ 3 × 20 - y = 10
⤇ 60 - y = 10
⤇ -y = 10 - 60
⤇ -y = - 50
⤇ y = 50
Hence,the present age of B will be 20 years and present age of A will be 50 years.