Question

The age of a and b are in the ratio 5 : 7. Four years from now the ratio of their ages will be 3 : 4. Then the present age of b is :

Answer 1

let present age of a be x years and b be years.
$\frac{x}{y} = \frac{5}{7} \\ 7x - 5y = 0......1$
$\frac{x + 4}{y + 4} = \frac{3}{4} \\ 4x + 16 = 3y + 12 \\ 4x - 3y = - 4.....2$
multiplying 1 with -3
$- 21x + 15y = 0....3$
multiplying 2 with 5
$20x - 15y = - 20......4$
adding 3 and 4
$- x = - 20 \\ x = 20$
put x=20 in 1
$7 \times 20 - 5y = 0 \\ - 5y = - 140 \\ y = \frac{ - 140}{ - 5} \\ y = 28$
therefore the present age of b 28 years
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Answer 2

Answer:

Present age of b will be 28

Step-by-step explanation:

Given:-the age of a and b is in the ratio be 5:7 & Four years from now the ratio of their ages will be 3 : 4.

To find:-the present age of b.

Solution:-

If A's age is 5x & B's age is 7x.

4 years later,

⇒ A will be 5x + 4 years old

⇒ B will be 7x + 4 years old

Now.

$\frac{5x+4}{7x+4}$=$\frac{3}{4}$....eq(i)

on solving eq(i) we get,

20x+16=21x+12

⇒x=4

So A and B age after 4 years will be,

a=5x+4=5(4)+4=24

b=7x+4=7(4)+4=32

∴Present age of b will be= 7x=7(4)=28

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