Question

the present ages of A and B are in the ratio 5 is to 6 three years ago , their ages were in the ratio 4 is to 5 find their present ages .​

Answer 1

Answer:

18yr 15yr

Step-by-step explanation:

three years ago the age of 4x,5x

now the present age will be

the present age of =4x+3

the present age of b=5x+3

=4x+3÷5x+3=5÷6

5(5x+3)=6(4x+3)

25x+15=24x+18

25x-24x=18-15

x=3

their present age will be

5x=5×3=15yr

6x=6×3=18yr

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