Question

The ratio of ages (in years) of A and B , 9 years ago, was 23:12. The ratio of their ages after 15 years will
be 35:24. What is the ratio of present ages of A and B ?​

Answer 1

Solution :-

Let,

Present age of A = x

Present age of B = y

9 years ago,

Age of A = x - 9

Age of B = y - 9

After 15 years,

Age of A = x + 15

Age of B = x + 15

According to the first condition :-

$\longrightarrow \sf \dfrac{x-9}{y-9}= \dfrac{23}{12}\\\\\longrightarrow 12(x-9)= 23( y-9)\\\\\longrightarrow 12x- 108 = 23y --207 \\\\ \longrightarrow 12x-23y = -99 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ..........................(1)$

According to the second condition :-

$\longrightarrow\sf \dfrac{x+15}{y+15}= \dfrac{35}{24} \\\\\longrightarrow 24(x+15) = 35 (y+15)\\\\\longrightarrow 24x+360 = 35y + 525 \\\\\longrightarrow 24x - 35y = 165 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ..........................(2)$

Multiply eq (1) by 2,

$\longrightarrow\sf 24x-46y = -198 \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ ..........................(3)$

Eq (2) - Eq (3),

$\longrightarrow \sf 11y = 363 \\\\\longrightarrow \bf y = 33$

Substitute the value of y in eq (1),

$\longrightarrow \sf 12x- 23 \times 33 = -99 \\\\\longrightarrow 12x -759 = -99 \\\\\longrightarrow 12x = 660\\\\\longrightarrow \bf x = 55$

Present age of A = 55 years

Present age of  B = 33 years

Answer 2

Step-by-step explanation:

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