The age of A and B are in the ratio 5:7 . 4 yrs from now the ratio of their ages will be 3:4. Find their present age.
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The ratio of their present ages = 5:7
Let present age of A = x and B = y
x/y = 5/7
7x = 5y
7x-5y = 0 → A
After 4 years
A's age = x+4
B's age = y+4
The ratio of their ages after 4 years = 3:4
⇒ (x+4)/(y+4) = 3/4
⇒ 4x+16 = 3y+12
⇒ 4x - 3y = - 4 → B
Simultaneous equation A and B
7x - 5y = 0
4x - 3y = -4
4(7x - 5y = 0)
7(4x - 3y = -4)
28x - 20y = 0
28x - 21y = -21
28x - 20y = 0
-28x + 21y = 21
⇒ y = 21
7x -5(21) = 0
7x = 105
x = 15
The present age of A is 15 and B is 21
Let present age of A = x and B = y
x/y = 5/7
7x = 5y
7x-5y = 0 → A
After 4 years
A's age = x+4
B's age = y+4
The ratio of their ages after 4 years = 3:4
⇒ (x+4)/(y+4) = 3/4
⇒ 4x+16 = 3y+12
⇒ 4x - 3y = - 4 → B
Simultaneous equation A and B
7x - 5y = 0
4x - 3y = -4
4(7x - 5y = 0)
7(4x - 3y = -4)
28x - 20y = 0
28x - 21y = -21
28x - 20y = 0
-28x + 21y = 21
⇒ y = 21
7x -5(21) = 0
7x = 105
x = 15
The present age of A is 15 and B is 21
Answered by
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Correct question:-
The present ages of A and B are in ratio 5:7. Four years from now the ratio of their ages will be 3:4. Find their present ages?
Given that :-
- 1. The present ages of A and B are in ratio 5:7.
- 2. Four years from now the ratio of their ages will be 3:4.
To find:-
- 1. Present age of A.
- 2. Present age of B.
Let the A's present age be 5x years.
And the B's present age be 7x years.
After 4 years,
A's age = 5x + 4 years
B's age = 7x + 4 years
Ratio = 3:4
Representing the condition mathematically,
(5x + 4/ 7x+ 4 = 3/4)
Cross multiplying,
=> 4 ( 5x + 4) = 3 ( 5x + 4)
=> 20x + 16 = 15x + 12
Transport the terms,
=> 20x - 21x = 12 - 16
=> - x = - 4
=> x = 4
Substitute x = 4 in the values of the ratio.
Hence, the present age of A is 20 years, and B's present age is 28 years.
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