Math, asked by Torsha11, 1 year ago

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.

Answers

Answered by Anonymous
1
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


Answered by xItzKhushix
2

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.

\huge{\sf{\boxed{\boxed{Solution}}}}

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.

\boxed{5\:x=5×4=20}

\boxed{7\:x=7×4=28}

Hence, the present age of A is 20 years, and B's present age is 28 years.

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