Question

Raman has two daughters Deepa and Anju present age of Raman is 9 more than that of twice the sum of Deepa and Anju 5 year hence the age of Raman will for more than the one and half times the sum of age of Deepa and Anju determine the age of Raman

Answer 1

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Answer 2

The present age of Raman is 29 years and sum of the age of his daughters Deepa and Anju is 10 years.

Step-by-step explanation:

Let the present age of Raman be 'x'.

Also Let the sum of present age of daughters Deepa and Anju be 'y'.

Now Given:

Present age of Raman is 9 more than that of twice the sum of Deepa and Anju.

framing in equation form we get;

$x = 2y +9\\\\x-2y = 9 \ \ \ \ equation \ 1$

Also Given:

5 year hence the age of Raman will four more than the one and half times the sum of age of Deepa and Anju.

framing in equation form we get;

$x+5 = 1\frac{1}{2}(y+10)+4$

On Solving the above equation we get;

$1\frac{1}{2}$ can be rewritten as $\frac{3}{2}$

Multiplying both side by 2 we get;

$2(x+5) = 2\times\frac{3}{2}(y+10)+4\times 2\\\\2x+10= 3(y+10)+8\\\\2x+10=3y+30+8\\\\2x-3y = 38-10\\\\2x-3y=28 \ \ \ \ equation\ 2$

Now Multiplying equation 1 by 2 we get;

$2(x-2y)= 9\times2\\\\2x-4y=18 \ \ \ \ equation \ 3$

Subtracting equation 3 by equation 2 we get;

$2x-3y- (2x-4y) =28-18\\\\2x-3y-2x+4y =10\\\\y =10$

Substituting the value of y in equation 1 we get;

$x-2y=9\\\\x-2\times 10 =9\\\\x-20=9\\\\x=9+20 =29 \ years.$

Hence the present age of raman is 29 years and sum of the age of his daughters Deepa and Anju is 10 years.