Question

The present age of A and B are in the ratio 5:6. Three years ago, their age were in the ratio 4:5 find their present ages.

Answer 1

Heya !!


Let present age of A and B be 5X and 6X.



three years ago age of A = ( 5X - 3 ) years.


Three years ago age of B = ( 6X - 3 ) years.


According to the question,



5x-3 : 6X -3 = 4:5



5 ( 5X - 3 ) = 4 ( 6X - 3 )


25X - 15 = 24X - 12



25X - 24X = -12+15



X = 3 years.


Present age of A = 5X = 5 × 3 = 15 years.


And,


Present age of B = 6X = 6 × 3 = 18 years.

Answer 2

GIVEN:-

Their present ages were in the ratio 5:6

Three years ago the ratio of their ages as 4:5

FIND:-

THEIR PRESENT AGES ?

SOLUTION:-

let, present age of A and B be x and y

now,

$\frac{x}{y} = \frac{5}{6}$

cross multiply

$x = \frac{5y}{6} ....(i)$

Before 3 years,

A's age (x-3) years

B's age (y-3) years

$\frac{x - 3}{y - 3} = \frac{4}{5}$

cross MULTIPLY

$5(x - 3) = 4(y - 3)$

$5x - 15 = 4y - 12$

$5x - 4y = - 12 + 15$

$5x - 4y = 3......(ii)$

$put \: x = \frac{5y}{6} \: in \: eq(ii)$

$5 \times (\frac{5y}{6} ) - 4y = 3$

$\frac{25y}{6} - 4y = 3$

$take \: lcm$

$\frac{25y - 24y}{6} = 3$

$\frac{y}{6} = 3 \\ y = 18$

$put \: y = 18 \: in \: eq(i)$

$x = \frac{5 \times 18}{6} \\ x = \frac{ \cancel{90}}{ \cancel{6} } = 15$

Hence, present age of A is = 15 yrs

and present age of B = 18 yrs