Question

14. The present of A and B are in the ratio 5:6. Three years ago, their ages were
in the ratio 4:5. Find their present ag​

Answer 1

Answer:

I think it should be 5 and 6 years old

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